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Equidistant Theorem – Theorem on Circles CBSE ICSE Class X

Published: 5 years ago

Category: CBSE, Education, Maths

Tags: , , , ,

Description:

Equidistant Theorem – Theorem on Circles CBSE  ICSE Class X

Equidistant Theorem – Theorem on Circles CBSE Class IX ICSE Class X – Theorem 3 – Equal chords of a circle are always equidistant from the centre by Ankit Mahajan for SuccessCDs Education Channel.

About this Video:

Given : Circle with Centre O
AB = CD
To Prove : OM = ON
Const : Join OA & OC

Proof : AB = CD (given)

OM is perpendicular to AB
AM = BM = ½ AB

ON is perpendicular to CD
CN = DN = ½ CD
We had AB = CD
AM = CN

In Δ OAM & ΔOCN
OA = OC (radii)
AM = CN (proved above)

OMA = ONC = 900 each
ΔOAM      ΔOCN (RHS congruency)

By CPCT
OM = ON

Hence Proved!

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