In the given figure from the point P two tangents PA and PB are drawn to a circle with centre O and ...........

Quantitative Aptitude ( CCS) Geometry

In the given figure, from the point P two tangents PA and PB are drawn to a circle with centre O and radius 5 cm. From the point O, OC and OD are drawn parallel to PA and PB respectively. If the length of the chord AB is 5 cm, then what is the value (in degrees) of ∠COD?

120

150

135

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Explanation:

AB = 5 (Given)
Radius = 5 (given)
Hence ?AOB is an equilateral triangle,
So,
θ = 60° = ∠BOM
because AO = OB = radius
∠AOB = 60
∠PAM = ∠PBM = 90 – 60 = 30 each
∠APB = 180 – (30 + 30) = 120 = ∠COD