Question

Proof of tangent is perpendicular to radius class 10

Answer 1

Hi there !!

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

Given :- XY is tangent to the circle Of at the point P

To prove :- XY perpendicular to OP

Construction :-Take any point R on XY different from P, Join OR.

Proof :- R is outside the circle.

OR >radius

OR >OP (OP=radius )

Therefore, OP is shortest distance from the point Of to the line XY

OP is perpendicular XY

Hence Proved

Thank you :)