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Center Angle Theorem – Theorem on Circles CBSE ICSE Class X

Center Angle Theorem – Theorem on Circles CBSE ICSE Class X

Center Angle Theorem  – Theorem on Circles CBSE Class IX ICSE Class X Theorem 7- In a circle angle subtended by an arc at the center is double the angle subtended by same arc at any other point on the circle by Ankit Mahajan for SuccessCDs Education Channel.

About this Video:

Given : Circle with Centre O
A, B & C are points on Circle.

To Prove: AOB = 2 ACB
Const: from C draw CM passing through O

Proof : In Δ AOC

Ext AOM = OAC + OCA (ext Angle property)
But OAC = OCA
(In a Δ equal sides have eq. angles opp. them)
AOM = 2OCA    (1)

In ΔOBC
Similarly,  BOM = 2 OCB   (2)

Adding 1 & 2

AOM  + BOM = 2 OCA + 2 OCB
= 2 (OCA + OCB)
AOB  = 2 ACB

Hence Proved!

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