Published: 5 years ago

Category: CBSE, Education, Maths

Tags: CBSE, ICSE, Learn Maths, Maths, NCERT

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 !