Question

3. In triangle ABC, the equation of side BC is x - y = 0. The
circumcenter and orthocenter of the triangle are (2, 3) and
(5,8), respectively. The equation of the circumcircle of the
triangle is
(1) x2 + y2 - 4x - 6y - 27 = 0
(2) r2 + y2 - 4x - y - 36=0
(3) r?+ y2 - 4x - 6y - 24 = 0
(4) x² + ² - 4x – by- 15=0

Answer 1

Reflection of orthocenter P(5,8) in BC(x−y=0) will lie on circumcircle.

Clearly P

1

≡(8,5). Thus, the equation of circumcircle with center O(2,3) and passing through P(8,5) is

(x−2)

2

+(y−3)

2

=(8−2)

2

+(5−3)

2

i.e, x

2

+y

2

−4x−6y−27=0

solution