Question

AB and CD are two equal chords of a circlewith centre 0 which intersect each other at right angle at point P. If OM I AB and ON I CD; show that OMPN is a square.​

Answer 1

Step-by-step explanation:

Clearly, all the angles of OMPN are 90° OM AB and ON CD

BM= 1/2 = AB= 1/2 CD= CN

(i) (Perpendicular drawn from the centre of a circle to a chord bisects it) intersect at point P inside

As the two equal chords AB and CD

The circle.. AP= DP and CP = BP

(ii) Now, CNCP = BMBP (by (i) and (ii))

⇒PN MP

Quadrilateral OMPN is a square

$\huge{ son \: prodigal}$