Class 10 Maths NCERT Solution-Chapter 10 Circles

This article for 10th Class Maths we will discuss theorem’s related to the Tangent.

Theorem No 2

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

Proof

Given Circle with center O

Point P outside the circle

Two tangents from point P, PQ and PR

To Prove PO=PR

Let’s join OP, OQ and OR

<OQP and <ORP formed are actually right angles, as per the theorem 1, angles between the radii and tangents are right angles.

= OQ=OR (radii of same circle)

= OP=OP (Common)

= Triangle OQP=Triangle ORP (RHS)

= PQ=PR (Hence proved)

Let’s take an alternative method also to solve using the Pythagoras theorem to prove the same.

Alternative method (Using Pythagoras theorem)

PQ²=OP²-OQ²

=OP²-OR²=PR² (As OQ=OR)

=PQ=PR (Hence proved)

We will now solve few CBSE NCERT solutions for Class 10 Maths

Exercise 10.1

Question 1. How many tangents can a circle have?

Solution:-Infinite

Continue.....> Class 10 Maths

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