Theorem 10.2 Class 10 Maths Explanation with Proof

In this post, we will discuss theorem 10.2 Class 10 Maths which is related to Chapter 10 Circles Class 10 Mathematics. After understanding theorem 10.2, you can solve the exercise questions given in the NCERT book of Class 10 Maths.

Theorem 10.2 Class 10 

The lengths of tangents drawn from an external point to a circle are equal.

Given 

AP and AQ are two tangents from point A to a circle O

To Prove 

AP=AQ

Construction 

Join OA, OP, and OQ

Proof 

AP is a tangent at P and OP is the radius through P.

∴    OP⊥AP 

Similarly, AQ is a tangent at Q and OQ is the radius through Q

∴    OQ⊥AQ 

In the right ∆OPA and ∆OQA, we have

OP=OQ (equal radii of the same circle)

AO=AO(common)

∠OPA=∠OQA (Each 90°)

∴∆OPA=∆OQA (By RHS congruence)

⟹    AP=AQ (By CPCT)

Hence AP=AQ    proved 

Related Topics

1. Theorem 10.1