SIR I AM NOT CLEAR

Dear Student,

 

Here is one simpler proof using direct result of the theorem given in the NCERT class 10 mathematics book that the tangent at any point of the circle is perpendicular to the radius through the pint of contact.

 

Given
PT is a tangent to a circle , A is the point of contact of the tangent with the circle

To prove
The perpendicular at the point of contact to the tangent to a circle passes through the centre.

Proof 
As we know that the tangent at any point of a circle is perpendicular to the radius through the point of contact and also the radius passes through the centre of the circle.

Thus it is proved that the perpendicular at the point of contact to the tangent to a circle passes through the centre.

Regards Topperlearning.