In a circle with centre

MATHEMATICS · Subjective · CBSE · Mathematics · Circles · Circles

Problem

O

, chords

AB

and

CD

are equal. Let the perpendiculars from

O

AB

and

CD

meet them at

M

and

N

respectively. (i) Show that

OM = ON

. (ii) Prove that

AM = MB

and

CN = ND

. (iii) If

AB = CD = 24\,\text{cm}

and the radius of the circle is

15\,\text{cm}

, find the length

OM