Question

Circles are drawn having the sides of triangle ABC as their diameters. Radical centre of the circles is the

• A. Circumcentre of triangle ABC
• B. In centre of triangle ABC
• C. Orthocentre of triangle ABC
• D. Centroid of triangle ABC

Answer 1

The correct option is C Orthocentre of triangle ABC

Radical centre: The radical axis of three circles taken in pairs meet at a point, called the radical centre of the circles.

Coordinates of radical centre can be found by solving the equations S1 = S2 = S3 = 0.

The radical centre of three circles described on the sides of a triangle as diameters is the orthocentre of the triangle.

If two circles cut a third circle orthogonally, then the radical axis of the two circles pass through the centre of the third circle.

The radical axis of the two circles will bisect their common tangents.