In the given figure, from the point P two tangents PA and PB are drawn to a circle with center 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?
Explanation:
In ∆AOB, AB = 5 = OA = PB
∴ ∆AOB is an equilateral triangle.
⇒ ∠AOB = 60°
In quadrilateral AOBP,
∠A = ∠B = 90°
∴ ∠AOB + ∠A + ∠B + ∠P = 360°
⇒ 60 + 90 + 90 + ∠P = 360
⇒ ∠P = 120°
Since PA || OC and PB || OD
⇒ ∠COD = ∠APB = 120°
Hence, option (b).
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