Theorem 10.1 Class 10 Maths Explanation with Proof

In this post, we will discuss theorem 10.1 Class 10 Maths which is related to Chapter 10 Circles Class 10 Mathematics. After understanding theorem 10.1, you can solve the exercise questions given in the NCERT book of Class 10 Maths.

 Theorem 10.1 Class 10 

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

Given 

A circle with centre O and a tangent AB to the circle at a point P

To Prove

OP⊥AB 

Construction 

Take any point R, other than P on the tangent AB. Join OR. Suppose OR meets the circle at Q.

Proof 

OP=OQ (Radii of the same circle)

But OP<OQ + QR

OP<OR

Thus OP is shorter than any other line segment joining o to any point of AB, other than P.

We know that among all line segment joining the point O to a point on AB, the shortest one is perpendicular to AB.

Hence 

OP⊥AB  proved 

Related Topics

1. Theorem 10.2