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Converse of Equidistant Theorem – Theorem on Circles

Converse of Equidistant Theorem – Theorem on Circles

Converse of Equidistant Theorem – Theorem on Circles CBSE Class IX ICSE Class X   –  Theorem 4 – Chords equidistant from centre are always equal by Ankit Mahajan for SuccessCDs Education Channel.

About this Video:

Given : Circle with Centre O
OM = ON
To Prove : AB = CD

Const : Join OA & OC

Proof : In ΔOAM & ΔOCN
OA = OC (radii)
OM = ON (given)
OMA = ONC = 900 each
ΔOAM       ΔOCN (RHS)

By CPCT : AM = CN

2AM = 2CN
AB = CD
(Line from centre perpendicular to a chord bisects the chord)

Hence Proved!

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