Question

If two circles intersect, prove that their common chord when produced bisects their common tangent.

Answer 1

Please check the attachment for a detailed solution.

When there are 2 circles that intersect, there is a chord formed in the area of intersection. When a tangent is drawn across the circles, it passes through the centre of the circles.

Since it passes through the centre, the tangent should be bisected by the chord in the area of intersection with an angle of 90° each that lies in between the chord and the tangent. It also shows that the centres of the circles lie on the bisector of the common chord.