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Class 10 Maths NCERT Solution-Chapter 10 Circles


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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