Question

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

Answer 1

XY = PQ = 8cm

In Circle O,

In Triangle POQ,

Ang. POQ = 120°,

Triangle POQ is an isoceles triangle (This is Property of Circles; OP, OQ are Radius inside a cirle),

Using the Sum of Angles of a Triangle, Angle OPQ = OQP = 30°

Triangle OXY,

This triangle is also an isoceles Triangle

Angle OXY = OYX = 30°

Therefore Angle XOY = 120°

Taking into consideration

Angle OXY = OPQ = 30°

Angle OYX = OQP = 30°

Angle POQ = XOY = 120°

OP = OQ = OX = OY (Radius of Circle)

Therefore, Triangle OXY and Triangle OPQ are Congruent.

So, XY = PQ = 8cm.