Question

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

Answer 1

Solution: In the given figure, QR is diameter and O is
centre. OP, SP and RP are lines touching the tangent at
the point of contact.
In triangles POS and POR
Line PS > PO and SO
Line PR > PO and RO
So, PS and PR are hypotenuses of respective triangles.
So, it is proved that Angle POR = Right Angle
If PO is increased to reach the other end of the perimeter, then it will be the diameter.