Question

Pls solve fast.....
In urgent need.

Prove that the perpendicular at the point of contact to the tangent to a circle passes through the centre..

Answer 1

Let O be the centre of the given circle.

AB is the tangent drawn touching the circle at A.

Draw AC ⊥ AB at point A, such that point C lies on the given circle.

∠OAB = 90° (Radius of the circle is perpendicular to the tangent)

Given ∠CAB = 90°

∴ ∠OAB = ∠CAB

This is possible only when centre O lies on the line AC.

Hence, perpendicular at the point of contact to the tangent to a circle passes through the centre of the circle.