Prove that the tangent at any point of a circle is perpendicular to the radius through the point of contact.

Question

Philoid · Accepted Answer

Given, A circle with centre O and with tangent XY at point of contact A.

To prove: OA ⊥ XY

From the figure,

OB > OC

OB > OA [⸪ OC = OA = radius]

Same will be the case with all other points on the circle.

But, among all the line segments, joining the point O to a point on XY, the shortest one is the perpendicular from O on XY.

⸫ OA ⊥ XY

Hence Proved.