Question

In a circle with centre O, PQ and XY are chords. If angle POQ=120°,angle OXY=30° and XY=8cm,then find PQ

Answer 1

PQ = 8cm

In Circle O,

In Triangle POQ,

Angle POQ = 120°,

POQ Being an isoceles triangle (Property of Circles),

Using sum of angles of a Triangle, Angle OPQ = OQP = 30°

Similarly, In Triangle OXY,

This triangle is also an isoceles Triangle

Angle OXY = OYX = 30°

Therefore Angle XOY = 120°

Angle OXY = OPQ = 30°

Angle OYX = OQP = 30°

Angle POQ = XOY = 120°

OP = OQ = OX = OY

Therefore, Triangle OXY and Triangle OPQ are Congruent.

So, XY = PQ = 8cm.