Question

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

Answer 1

Answer:

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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