[tex] \bigstar \: \underline{ \underline{ \tt{Question}}} : [/tex] In the given figure , M and N are the centres of two intersecting circles. Prove that :
i. PQ [tex] \perp[/tex] MN
ii. PR = RQ

~Thanks in advance! <3

[tex] \bigstar \: \underline{ \underline{ \tt{Question}}} : [/tex] In The Given Figure , M And N Are

Answers

Answer 1

Answer:

See Below.

Step-by-step explanation:

We are given two intersecting circles with centers M and N.

And we want to prove that: I) PQ ⊥ MN and that II) PR = RQ.

Since MP and MQ are radii of the same circle:

[tex]MP\cong MQ[/tex]

Likewise, since NP and NQ are radii of the same circle:

[tex]NP\cong NQ[/tex]

And by the Reflexive Property:

[tex]PQ\cong PQ[/tex]

Therefore, by SSS Congruence:

[tex]\Delta MPN\cong \Delta MQN[/tex]

By CPCTC:

[tex]\displaystyle \angle PMN\cong \angle QMN[/tex]

And by the Reflexive Property:

[tex]MR\cong MR[/tex]

And since they are the radii of the same circle:

[tex]MP\cong MQ[/tex]

Therefore, by SAS Congruence:

[tex]\Delta MPR\cong \Delta MQR[/tex]

Therefore, by CPCTC:

[tex]PR\cong RQ[/tex]

Note that PQ is a chord in Circle M.

Therefore:

[tex]\text{Segment $MN$ bisects chord $PQ$}[/tex]

In a circle, a segment that passes through the center of the circle that is perpendicular to a chord also bisects the chord.

And conversely, a segment that passes through the center of a circle that bisects a chord in the circle is also perpendicular to the chord.

So:

[tex]\displaystyle PQ\perp MN[/tex]

Answer 2

Answer:

Step-by-step explanation:

First step is to prove triangle MPN ad MQN are congruent.

MP=MQ, radius of circle M

NP=NQ, radius of circle N

we have two S in SAS  and for A, we need to prove angle MPN = MQN

consider triangle QMP, it is isosceles so angle MPQ = MQP

consider triangle QNP; it is isosceles so angle  QPN = PQN

combining the two above

angle MPN = MPQ+QPN = MQP+PQN = MQN

By SAS, triangle MPN and MQN are congruent

By symmetry, MN is perpendicular to PQ

It also disects PQ so PR = RQ


Related Questions

Please help
Which one is correct?

Answers

Answer:

The first one

Step-by-step explanation:

3/5 and 9/25

Learning task 3
What polygon is being described in the picture

Answers

There isn’t a picture, can you post one?

The average number of slam dunks between the sophomore basketball league members is 20. The average number of slam dunks between the sophomore and junior basketball league members is 30. If there are 40 members in the sophomore league and 20 members in the junior league, how many slam dunks are made in the junior league?

Answers

Answer:

The sum of the slam dunks made in the junior league is 1,000 slam dunks

Step-by-step explanation:

The known parameters are;

The average number of slam dunks between the sophomore basketball league members, μ₁ = 20

The average number of slam dunks between the sophomore and junior basketball league members, μ₃ = 30

The number of members of the sophomore league, n₁ = 40

The number of members of the junior league, n₂ = 20

We get;

The sum of the scores of the sophomore league members, S₁ = μ₁ × n₁

∴ S = 20 × 40 = 800

The sum of the scores of the sophomore and junior league members combined, S₃ = (n₁ + n₂) × μ₃

∴ S₃ = (40 + 20) × 30 = 1,800

The sum of the slam dunks made by the junior league members, S₂ = S₃ - S₂

∴ S₂ = 1,800 - 800 = 1,000

∴ The sum of the slam dunks made in the junior league, S₃ = 1,000

A rescue team 1000 ft. away from the base of a vertical cliff measures the angle of elevation to the top of the cliff to be 70. A climber is stranded on a ledge. The angle of elevation from the rescue team to the ledge is 55. How far is the stranded climber from the top of the cliff?

Answers

The stranded climber is 14 ft from the top of the cliff. You are going to subtract the top of the cliff from the ledge and 14 is your answer.

The top of a pie container is a circle. The radius of the pie is 8 inches and the radius of the container is 9 inches. What is the difference between the circumference of the container and the circumference of the pie in inches to the nearest tenth?
A : 3.1 inches
B 6.3 inches
C: 12.6 inches
D 25.1 inches
E 50.2 inches

Answers

Answer:

B. 6.3 inches.

Step-by-step explanation:

I'll use 2πr for both sides of this.

Pie:

2 * 3.14 * 8

16 * 3.14

50.24 inches for the pie

Container:

2 * 3.14 * 9

18 * 3.14

56.52 inches for the container

Difference:

56.52 - 50.24

6.28-inch difference, which rounds to 6.3 inches. B is our answer.

hi help please! i’m struggling lol i already know the first part

Answers

Answer:

180 Degrees minus 117= sixty three

answer is x is 63

Where did I get the 180?

- straight Angles have 180

- 117 is a part of 180

-so that is why you had to subtract

I hope this Helps You!!

A right triangle is a triangle with two angles. True or false?

Answers

Answer:

The answer is false.

Step-by-step explanation:

A triangle would also be opposite to a angle of property.

False- A right triangle is a triangle with right degree angles of

50 points
Please help ///// brainiliest
A 6 cm high cone has a volume of 128π cm3 What is its exact surface area?

A. 160π cm2
B. 96π cm2
C. 144π cm2
D. 104π cm2

Answers

Answer:

height [h]=6cm

Volume of cone =1/3 πr²h

128πcm³=1/3×π×r²×6

128×3/6=r²

r=√64

r=8cm

Now

slant height (l)=√{8²+6²}=10cm

again

.Total surface area :πrl+πr²=π×8(10+8)=144πcm²

its exact surface area is C. 144π cm²

[tex]\green{\boxed{-answer-}}[/tex]

Thats kinda hard but here maybe this one

C) 104π cm2

I dont really know well have a nice day man

Hey can you help me fast!!

Answers

Answer: -6.3 lb after 3.5 hours

Step-by-step explanation:

-1 (4)/(5) = -9/5 = -1.8

0.5hr = -0.9

1hr = -1.8

2hr=-3.6

3hr=-5.4

3.5hr = -6.3

Select all equations whose graphs have a vertex with x-coordinate 2

A. y=(x-2)(x-4)
B. y=(x-2)(x+2)
C. y=(x-1)(x-3)
D. y=x(x+4)
E. y=x(x-4)

Answers

Answer:

C

Step-by-step explanation:

because you have to foil then do -b/2a

By finding the x-coordinate of each vertex, we will see that the correct options are C and E.

How to identify the x-value of the vertex?

For a quadratic equation of the form:

y = (x - a)*(x - b)

Where a and b are the roots, such that a < b, the x-value of the vertex is given by:

a + (b - a)/2

With that, we can check the x-value of the vertex of each option.

A) y=(x-2)(x-4)

The x-value of the vertex is:

2 + (4 - 2)/2 = 3

B)  y=(x-2)(x+2)

The x-value of the vertex is:

-2+ (2 - (-2))/2 = 0

C)  y=(x-1)(x-3)

The x-value of the vertex is:

1 + (3 - 1)/2 = 2

D) y = x(x+4) = (x - 0)*(x + 4)

The x-value of the vertex is:

-4 + (0 - (-4))/2 = -2

E)  y=x(x-4) = (x - 0)*(x - 4)

The x-value of the vertex is:

4 + (0 - (4))/2 = 2

So the two options that have a vertex with x-coordinate 2 are options C and E.

If you want to learn more about quadratic equations, you can read:

https://brainly.com/question/1214333

Anyone please??? I need the help my teachers sent me this packet and I know nothing :////

Answers

Answer:

Step-by-step explanation:

Translation:

A: (1.2)

B: (2,2)

C: (2,4)

answer for brainilest and 30 points.

Answers

Answer:

Top Right

Step-by-step explanation:

231/pi(3)^2 =8.17

Round down to 8

Answer:

The height is 8 inches

Step-by-step explanation:

Well to find the volume of a cylinde like this, he formula is Base * height.

To find the base we need to find the area of the circle.

a=πr^2

The radius is 3 inches, 3^2=9

Since π is suppose to be 3.14 multiply

9*3.14= 28.26

We know that the cylinder can hold 231 cubic inches. So technically it can fill (x) 28.26 inches.

solve the equation

28.26x=231

Divide

231/28.26

The answer would be about 8 inches

On a bicycle ride,Betty rode 7 miles in 2 hours. At the same rate of speed,how far could she ride in 8 hours?Please hurry

A.14 miles

B.16 miles

C.20 miles

D.28 miles

E.56 miles

Answers

D 28 miles you want to multiply by 4 so 7x4 =28

please help me find the trend line for the scatterplot!

Answers

Answer:

wbv wncwic wndv envne jcsid ejshf vuia csiubc wcbu

Answers?????????????

Answers

Answer:

a)

-7-128

Step-by-step explanation:

b) plot your graph using the table of value

c) draw a line at 2.5 on the x-axis

Answer:

the picture above ⬆️ is for the gaps in the table of values y= -7,-4,-1,2,5,8

b: using a scale of 1cm to represent 1 unit on both axis

Step-by-step explanation:

on the graph using the table of values. ...plot a graph using.a scale that will be ok for the value for example 1cm to represent 1 unit or 2cm to represent 1 unit

Find the center and radius of the circle:
x2 + y2 + 14x – 2y + 25 = 0

Answers

Center =(-7, 1)
Radius = 5

Solve for x.
2x2 + x = 10

Answers

Answer:

x = 2, x = -5/2

Step-by-step explanation:

2x² + x - 10 = 0

(2x + 5)(x - 2) = 0

2x + 5 = 0

2x = -5

x = -5/2

x - 2 = 0

x = 2

Select the correct answer from each drop-down menu.
The table shows the number of games a chess player won in professional competitions, based on the number of games played.

Games Played (x) 10 15 20 25 30
Games Won (y) 4 10 16 21 25
The line of best fit for the situation is
___.

If the chess player plays 40 games in the next competition, the expected number of games won would be approximately __.
???

Answers

Answer:

36 games won ...............

Answer:

y=1.06x-6

36

Step-by-step explanation:

Can you please help!!

Answers

I can confirm the answer is B but another person already answered it so I might not take all the credit

Can you solve the surface area and the volume for the triangular prism? i need it now please​

Answers

Surface Area = 96in³

To find the surface area of a triangular prism we can use the following equation

[tex]SA = Perimeter * Height[/tex]

The perimeter is the perimeter of one base, and the height is the length of the lines connecting both bases. Now that we know that we can input that into the equation

[tex]SA = (5 + 4 + 3)8\\SA = (12)8\\SA = 96\\[/tex]

20% of ______ is 120​

Answers

Answer:600

Step-by-step explanation:

Answer:

20

___ x X = 120

100

x100       x 100

20x = 120

divide by 20 on both sides.

x = 6

Marilyn Manson anybody else a fan ?​

Answers

Answer:

wait who is that again?

Step-by-step explanation:

Answer:

 Yes, I am a fan.

Step-by-step explanation:

;)

kirans aunt is 15 years older than kiran. how old will kirans aunt be when kiran is 13? how old will kiran be when his aunt is 60 years old?

Answers

Answer:

When Kiran is 13, his aunt will be 28.

When Kiran's aunt is 60, he will be 45.

Step-by-step explanation:

Hope this helps!

Answer:

a) 28 (kiran's aunt when kiran is 13)

b) 45 (kiran when kiran's aunt is 60)

Step-by-step explanation:

first

let kiran's age be k

kiran's aunt= 15 + k

when kiran is 13, kiran's aunt is 15+13

15+13= 28

when kiran's aunt is 60;

15+k = kiran's age

60 = 15+ k

k = 60-15

k = 45

What number must you add to complete the square?
X2 + 12x = 40
x2
o
A. 36
B. 20
(
C. 6
O
O
D. 5
х

Answers

Answer:

36

Step-by-step explanation:

x^2 + 12 x  = 40

To complete the square, take the coefficient of the x term

12

Divide by 2

12/2 = 6

Square it

6^2 = 36

Add 36 to each side

If you have 2 cans of tomato soup, 3 cans of chicken soup, 2 cans of cheese soup, 2 cans of potato soup and 1 can of beef soup what is the probability that he will choose a ca of tomato and a can of cheese soup

Answers

Answer:

1/25

Step-by-step explanation:

Probability calculates the likelihood of an event occurring. The likelihood of the event occurring lies between 0 and 1. It is zero if the event does not occur and 1 if the event occurs.

probability of choosing a can of tomato and a can of cheese soup = probability of choosing a can of tomato x probability of choosing a can of cheese soup

total number of cans = 2 + 3 +2 + 2 + 1 = 10

probability of choosing a can of tomato = number of can of tomato / total number of cans

= 2/10 = 1/5

probability of choosing a can of cheese soup = number of can of cheese soup / total number of cans

= 2/10 = 1/5

1/5 x 1/5 = 1/25

Solve the system of equations x+2y=-16 and x+6y=-28 by combining the equations.

Answers

Answer:

x= -18 y=-5/3

Step-by-step explanation:

Answer:

x = -10

y = -3

Step-by-step explanation:

When combining the equations, we must ensure that one of the two variables will cancel out. The easiest way to do this will be to multiply one of the equations by -1, such that the x will cancel out once they are added together. This can be done with either equation, but I will do it for the first one.

This gives us the system:

[tex]\left \{ {{-x-2y=16} \atop {x+6y=-28}} \right.[/tex]

We can then add the two equations by combining each of the terms:

[tex](x - x) + (6y - 2y) = (-28 + 16)\\(0) + (4y) = (-12)\\4y = -12\\y = -3[/tex]

Now that we have the value for y, we substitute it back into any of the original equations and solve for x:

[tex]x + 2y = -16\\x + 2(-3) = -16\\x - 6 = -16\\x = -10[/tex]

To check our work, we substitute both x and y into the other original equation:

[tex]x + 6y = -28\\(-10) + 6(-3) = -28\\-10 - 18 = -28\\-28 = -28[/tex]

HELPP will give brainliest NO LINKSSS

Answers

Answer:

you didnt attach anything

Step-by-step explanation:

The third quartile value for the
data set shown in the box plot
below is:
65
70
75
80
85
90

Answers

Answer:

85

Step-by-step explanation:

The q1 is 7-, q2 is 77.5 and the third quartile range is 85

Mancini's Pizzeria sells four types of pizza crust. Last week, the owner tracked the number sold of each type, and this is what he found. Type of Crust Number Sold Thin crust Thick crust Stuffed crust Pan style Based on this information, of the next pizzas he sells, how many should he expect to be thick crust? Round your answer to the nearest whole number. Do not round any intermediate calculations.

Answers

The complete exercise with the answer options is as follows:

Mancini's Pizzeria sells four types of pizza crust. Last week, the owner tracked the number sold of each type, and this is what he found.

Type of Crust Number Sold

Thin crust            364

Thick crust             240

Stuffed crust             176

Pan style            260

Based on this information, of the next 3000 pizzas he sells, how many should he expect to be thick crust? Round your answer to the nearest whole number. Do not round any intermediate calculations.

Answer:

692 thick crust pizzas

Step-by-step explanation:

With the data given in the exercise, we must first find the total number of pizzas, then we must find the proportion between the thick crust pizzas and the total number of pizzas, finally we must propose a rule of three to find the new proportion of crust pizzas thick on a total of 3000 pizzas.

Type of Crust Number Sold

Thin crust            364

Thick crust             240

Stuffed crust             176

Pan style            260

total pizzas  : 1040

Now we must calculate for 3000 pizzas how much would be the total of thick crust pizzas.For that we must use the relationship found, that is, in 1040 pizzas there are 240 thick crust pizzas

1040→240

3000→x

x= [tex]\frac{3000x240}{1040}[/tex] = 692

Now we have a new proportion that out of 3000 pizzas there are a total of 692 thick crust pizzas

There are 22,521 more people living in the suburbs of a city than in the city. If 17,245 people live in the​ city, how many people live in the​ suburbs?

Answers

Answer:

Number of people in the suburbs= 39,766

Step-by-step explanation:

Giving the following information:

22,521 more people are living in the suburbs of a city than in the city.

Number of people in the city= 17,245

To calculate the number of people that lives in the suburbs, we need to use the following formula:

Number of people in the suburbs= Number of people in the city + 22,521

Number of people in the suburbs= 17,245 + 22,521

Number of people in the suburbs= 39,766

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