Question

In Fig. 10.89, if tangents PA and PB are drawn to a circle such that ∠APS = 30° and chord AC is drawn parallel to the tangent PB, then ∠ABC =
A. 60°
B. 90°
C. 30°
D. None of these

Answer 1

∠ABC = 30°

Solution :-

Given :-

∠APB = 30°

∵ Tangents PA and PB are equal

∴ ∠PBA = ∠PAB = x

x + x + 30 = 180

2x + 30 = 180

2x = 150

x = 75°

∵ AC || PB

∴ ∠ABP = ∠CAB = 75° (Alternate Interior Angles)

Also,

∠ABP = ∠ACB = 75° (Alternate Segment Theorem)

Now,

∠ACB + ∠CAB + ∠ABC = 180°

75 + 75 + ∠ABC = 180

∠ABC = 180 - 150

∴ ∠ABC = 30°

So, answer is option (c) 30°