Question

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

Answer 1

Answer:

lets take a circle with centre o and a tangent XY

to the circle at a point Pb. now prove that OP is perpendicular to XY.

take a point Q on XY other than P and join OQ.

the point Q must lie outside the circle. note that if Q lies inside the circle, XY will become a secant and not tangent to the circle. therefore o q is longer than the radius of the circle that is OQ is greater than OP. SINCE THIS HAPPENS FOR EVERY POINT ON THE LINE X Y ACCEPT THE POINT P, OP IS THE SHORTEST OF ALL THE DISTANCES OF THE POINT OF TO THE POINT OF XY. CEO AP IS PERPENDICULAR TO XY.

HEYA DRAW THE DIAGRAM ACCORDINGLY

Answer 2

Answer:

Step-by-step explanation:

Pls refer the pic