Question

If the circumcentre of the triangle with
vertices (a, -1), (6, -9) and (10, b) is (6,-5),
find the values of a and b.​

Answer 1

Answer:

Let, (x, y) be the coordinates of the circumcenter.

D1 be the distance from the circumcenter to vertex A

D2 be the distance from the circumcenter to vertex B

D3 be the distance from the circumcenter to vertex C

Answer 2

Let x1,x2 and x3 be a,6,10 respectively.

Let y1,y2 and y3 be -1,-9,b respectively.

For x = x1+x2+x3/3

6 = a+6+10/3

6 × 3 = 16+a

18 = 16+a

18-16 = a

a = 2

For y = y1+y2+y3/3

-5 = (-1)+(-9)+b/3

-5 = -1-9+b/3

-5×3 = -10+b

-15 = -10+b

-15+10 = b

b= -5