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Converse of a Perpendicular Theorem – Theorem on Circles

Published: 4 years ago

Category: CBSE, Education, Maths

Tags: , , , ,

Description:

Converse of a Perpendicular Theorem – Theorem on Circles

Converse of a Perpendicular Theorem – Theorem on Circles CBSE ICSE Class X. In a circle a line drawn from centre of a circle bisecting a chord is always perpendicular to the chord by Ankit Mahajan for SuccessCDs Education Channel.

About this Video:

Given – Circle with Centre O and Chord AB
OD bisects AB
i.e., AD = BD

To Prove  – OD is perpendicular to AB
Const    –    Join OA & OB

Proof –  Δ ODA & Δ ODB

OA = OB (radii)
OD = OD (common)
AD = DB (given)
ΔODA  Δ ODB (SSS Congruency)
By CPCT ADO = BDO

But,
ADO + BDO = 1800 (LP)
2 ADO = 1800
ADO = 90

BDO = 900 OD is perpendicular to AB

Hence Proved !

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