Theorem 10.3 Class 9 Maths Explanation with Proof

Today, we will discuss theorem 10.3 class 9 Maths which is related to Chapter 10 Circles Class 9 Mathematics. After understanding theorem 10.3, you can solve the exercise questions given in the NCERT book of Class 9 Maths.

 Theorem 10.3 Class 9

The perpendicular from the centre of a circle to a chord bisects the chord.

Given 

AB is a chord of a circle with centre O and OM⊥AB.

To Prove 

OM bisects AB

i.e.   AM=MB

Construction 

Join OA and OB

Proof 

In ∆AMO and ∆BMO, we have

OA= OB                 (Radii of same circle)

∠AMO=∠BMO    (Each 90°)

And OM=OM       (Common sides)

∴ ∆AMO=∆BMO  (By RHS congruence)

⟹AM=MB           (BY CPCT)

i.e.     OM bisects AB   Hence proved

 

Related Topics

1. Theorem 10.2

2. Theorem 10.4