Question

prove that A(4,5) , B(4,2), C (8,2) represents the vertices of a right angled triangle . Find the coordinate of the circumcentre . What is the radius of the circumcircle?

Answer 1

Distance between (4, 5) and (4, 2) = 5 – 2 = 3

Distance between (4, 2) and (8, 2) = 8 – 4 = 4

= √(4 8)² + (5 2)²= √ 4² 3²= 5

3, 4, 5 are sides of a right angled triangle, since 3² + 4² = 5²

The coordinate of circumcircle is (6,3,5)

Radius of circumcircle = 2.5 unit