Theorem 10.1 : The tangent at any point of a circle is perpendicular to the radius through the point of contact.
Given: A circle with center O has a tangent XY at point of contact P on the circle.
To Prove: OP ⊥ XY
Proof: Let Q be a point on XY, Connect OQ.
it touches the circle at R
Hence,
OQ > OR
OQ > OP ( OP and OR are the radii of same circle)
Same will be the case with all other points on circle
So, OP is the smallest line that connects XY and the smallest line is perpendicular to the tangent.
∴ OP ⊥ XY