Published: 4 years ago

Category: CBSE, Education, Maths

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

Description:

Theorem on Circles CBSE Class IX ICSE Class X (Perpendicular Theorem)

Circles

Theorem!

In a circle a line drawn from centre of a circle ^ to a chord bisect the chord.

Given

Circle with centre OD chord AB.

OD ^ AB

To Prove AD = DB

Const We join OA DOB

Proof In Angle OAD Angle OBD

OA = OB (radii of circle)

OD = OD (Common)

Angle ODA = Angle ODB 90° each (OD ^ AB)

Angle OAD = Angle OBD (RHS Congruency)

By CPCT

AD = DB

Hence Proved!