Question

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

Answer 1

PQ = 8 cm , if  In a circle with centre O, PQ and XY are chords.  ∠ POQ=120°, ∠OXY=30° and XY=8 cm,

Step-by-step explanation:

circle with centre O

PQ and XY are chords

∠POQ = 120°

OP = OQ = Radius

=> ∠OPQ = ∠OQP

∠OPQ + ∠OQP + ∠POQ  = 180°

=> ∠OPQ + ∠OQP +  120°  = 180°

=> ∠OPQ + ∠OQP  = 60°

=> ∠OPQ = ∠OQP = 30°

∠OXY = 30°

OX = OY = Radius

=> ∠OXY = ∠OYX

=> ∠OYX = 30°

∠OXY + ∠OYX  + ∠XOY = 180°

=> ∠XOY = 120°

ΔPOQ & ΔXOY

OX = OY = OP = OQ = Radius

∠OPQ = ∠OQP =  ∠OXY = ∠OYX

∠POQ = ∠XOY

=>ΔPOQ ≅ ΔXOY

=> PQ = XY

XY = 8 xm

=> PQ = 8 cm

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