Question

Proof of a tangent is perpendicular to the radius

Answer 1

Answer:

Here is the answer it is a basic questions

Answer 2

$OP \perp XY$

Step-by-step explanation:

Let a circle with centre O, with XY being tangent at P on its circumference.

Now, let have XY a tangent at point P.

To Prove - $OP \perp XY$

Proof - Suppose Q a point on XY such that on joining OQ, R is the point of intersection of OQ and circumference.

Hence, OQ > OR and OQ > OP (OP = OQ = Radius of Circle)

We will see the same situation with rest all points (if any) on the circle.  

Finally, we can say that OP is the smallest line that connects XY.

Hence, OP is smallest line that connects XY and the smallest line is Perpendicular.

So, $OP \perp XY$