Question

4. In a circle with centre O, PQ and XY are chords. If
Z POQ = 120°, Z OXY = 30° and XY = 8 cm, then find PO.
ating chords of a circle make equal angles​

Answer 1

PO = 8/√3  cm

Step-by-step explanation:

in Δ POQ

OP = OQ  ( radius)

=> ∠OPQ = ∠OQP

Sum of angles of triangle = 180°

∠POQ + ∠OPQ + ∠OQP = 180°

=> 120° + ∠OPQ + ∠OQP = 180°

=> ∠OPQ + ∠OQP = 60°

∠OPQ = ∠OQP = 30°

in Δ XOY

OX = OY = Radius

∠OXY = ∠OYX = 30°

=> ∠XOY = 120°

in Δ POQ & Δ XOY

PO = XO   Radius

OQ = OY  Radius

∠POQ = ∠XOY = 120°

=> Δ POQ ≅ Δ XOY

=> PQ = XY

PQ = 8 cm

PQ² = OP² + OQ² - 2OP * OQ Cos∠POQ

=> 8² = OP² + OP² - 2OP²Cos120°

=>  8² = OP² + OP² - 2OP²(-1/2)

=> 8² = OP² + OP² + OP²

=> 3OP² = 8²

=> OP = 8/√3

=>  PO = 8/√3  cm

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