Question

Circles M and K are congruent, QR LN p ≅ p and OP VW p ≅ q . Find x and y.

Answer 1

If QR = LN, that is, x + y = 6;
And OP = VW, that is, 3x - y = 10;

You can solve this system of equations. I will solve by the substitution method.

{x + y = 6 -> y = 6 - x
{3x - y = 10

{3x - y = 10
-> 3x - (6 - x) = 10
-> 3x - 6 + x = 10
-> 4x = 10 + 6
-> 4x = 16
-> x = 16/4
-> x = 4

{y = 6 - x
-> y = 6 - 4
-> y = 2

Answer: X = 4; Y = 2.

Answer 2

`x=4`

`y=2`

Explanation:

We have been given an image of two congruent circles. We are asked to find the value of x and y for our given circles.

Since
`\overline{QR}\cong\overline{LN}`, so
`\overline{QR}=\overline{LN}`.

`x+y=6...(1)`

Since
`\overline{OP}\cong\overline{VW}`, so
`\overline{OP}=\overline{VW}`.

`3x-y=10...(2)`

From equation (1), we will get:

`x=6-y`

Upon substituting this value in equation (2), we will get:

`3(6-y)-y=10`

Upon using distributive property, we will get:

`18-3y-y=10`

`18-4y=10`

`18-18-4y=10-18`

`-4y=-8`

`(-4y)/(-4)=(-8)/(-4)`

`y=2`

Therefore, the value of y is 2.

Now, we will substitute
`y=2` in equation (1) as:

`x+2=6`

`x+2-2=6-2`

`x=4`

Therefore, the value of x is 4.