Question

3. Find the circumcenter of triangle EFG with E(2,6), F(2,4), and G(6,4)

(4,4)
(5,4)
(4,5)
(2,5)​

Answer 1

(4,5)

Explanation:

We are to find the circumcenter of triangle EFG with vertices

E(2,6), F(2,4), and G(6,4)

Let S(x,y) be the circum center. Then this point is equidistance from E, F and

G

i.e.
`ES=FS=GS\\ES^2 =FS^2 =GS^2`

`(x-2)^2+(y-6)^2 =(x-2)^2+(y-4)^2 =(x-6)^2+(y-4)^2 \\i.e. x^2-4x+4+y^2-12y+36 = x^2-4x+4+y^2-8y+16 = x^2-12x+36+y^2-8y+16 \\4y = 20: y =5\\8x=32\\x=4`

Thus circumcenter is (4,5)