Question

3. Find the center of the circle that can be circumscribed about EFG with E(6,4), F(6,2), and G(10,2).

A. (6, 4)
B. (8,3)
C. (3,8)
D. (4,2)

Answer 1

B is the correct answer

Answer 2

Step-by-step explanation:

The general form of the equation of a circle is

(x-a)^2 + (y-b)^2 = r^2 where the center is (a,b)

Plugging in the given values:-

(6 - a)^2 + (4-b)^2 = r^2 and

(6-a)^2 + (2-b)^2 = r^2

Subtracting:-

(4-b)^2 - (2 - b)^2 = 0

16 - 8b + b^ - (4 -4b + b^2) = 0

12 - 4b = 0

-4b = -12

b = 3

Similarly if we take the 2 points (6,2) and G(10,2) and make two equations we can find the value of a

(6-a)^2 + (2-b)^2 = r^2

(10.a)^2 + (2-b)^2 = r^2 subtract::-

(6-a)^2 -(10-a(^2 = 0

this will give a = 8

so the center of the circle is the poit (8,3)