In a circle with centre

MATHEMATICS · Subjective · CBSE · Mathematics · Circles · Circles

Problem

O

, let

AB

and

CD

be two chords such that the perpendicular distances from

O

to the chords are equal. (i) From

O

drop perpendiculars

OM

and

ON

AB

and

CD

respectively. Show that

\triangle OMA \cong \triangle ONC

. (ii) Using the result of part (i) or otherwise, prove that

AB = CD

. (iii) State the converse of the statement proved in part (ii).