Two tangents AP and AQ are drawn to a circle with centre O from an external point A, where P and Q are points on the circle. If AP = 12 cm and ∠PAQ=60°, then the length of chord PQ is:
Answer & explanation
Correct answer: option 1
We know that,
sin A = Perpendicular/Hypotenuse
tan A = Perpendicular/Base
We have,
AP = 12 cm
∠PAQ = 60°
In OPAQ,
∠OPA + ∠OQA + ∠PAQ + ∠POQ = 360°
= 90° + 90° + 60° + ∠POQ = 360° - 240°
= ∠POQ = 120°
= ∠POA = 120°/2
= ∠POA = 60°
In ΔOPA
tan 60 = PA/OP
= √3 = 12/OP
= OP = 12/√3
= OP = 4√3
In ΔOPM
sin 60 = PM/OP
= √3/2 = PM/4√3
= PM = (√3/2) 4√3
So, PM = 6
= PQ = 2PM
= PQ = 2 × 6
= PQ = 12 cm