In the given figure, AOB is a diameter of a circle and CD || AB.

Question:

In the given figure, AOB is  a diameter of a circle and CD || AB. If BAD = 30°, then ∠CAD = ?
(a) 30°

(b) 60°
(c) 45°
(d) 50°

Solution:

(a) 30°
∠ADC = ∠BAD = 30°     (Alternate angles)
∠ADB = 90°                    (Angle in semicircle)
∴ ∠CDB = (90° + 30°) = 120°
But ABCD being a cyclic quadrilateral, we have:

∠BAC + ∠CDB = 180°
⇒ ∠BAD + ∠CAD + ∠CDB = 180°
⇒ 30° + ∠CAD  + 120° = 180°
⇒ ∠CAD  = (180° - 150°) = 30°

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