Question

proue that "the Tangent at any
point of a circle is perpendicular
to the radius through the point
of contact"​

Answer 1

Answer:

we are given a circle with centre o and a tangent xy to the circle at a point P.

Explanation:

1. To prove ÷ OP perpendicular to XY.

proof ÷ Take a point Q on XY and join OQ.

The point Q must lie outside the circle.

Therefore , OQ is longer than the radius OP.

Since this happens for every point on the line XY except P, OP is the shortest of all the distances of the point O to the points of XY.

So, OP is perpendicular to XY.