Question

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

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

hope this helps you

Answer 2

Sorry I don't know what to write