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SSC CPO 2019 PYQ — Question 141

SSC CPO Tier I - 13th December 2019 - Shift 2 • Quantitative Aptitude • Q141

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ABCD is a cyclic quadrilateral. The tangents to the circle at the points A and C on it, intersect at P. If ∠ABC = 98°, then what is the measure of ∠APC?

Show answer & explanation

Correct answer: C

Explanation

The correct answer is Option 3 i.e. 16°

Understanding Application
Tricks

According to question:
Now

Since ∠B and ∠D are the opposite angles of a cyclic quadrilateral

So,

∠B + ∠D = 180

⇒ ∠D = 180 - 98

⇒ ∠D = 82

So,

Let centre is O

∠AOC = 2 × ∠D

∠AOC = 164

Here In quadrilateral AOCP:

Sum of all angle = 360

Hence,

⇒ ∠AOC  + ∠OCP + ∠ACP + ∠CAO = 360

⇒ 164 + 90 + ∠ACP + 90 = 360

⇒ ∠ACP = 360 - 344

⇒ ∠ACP = 16