PAQ is a tangent to circle with centre O at a point A on it AB is a chord such that C is a point on ...........

Quantitative Aptitude (CGL) Geometry

PAQ is a tangent to circle with centre O, at a point A on it. AB is a chord such that . C is a point on the

major arc AB such that . If , then the value of is:

This questions was previously asked in

SSC CGL 9th March 2020 Shift-3

112

110

116

Let’s break down what’s really happening:

- PAQ is a tangent at A, which means the angle between tangent PAQ and chord AB at A equals the angle in the alternate segment, which is angle ACB.

- Angle between the tangent and chord = ?BAQ.

- Angle subtended by the chord in the major arc = ?ACB.

- By the tangent-chord theorem: ?BAQ = ?ACB.

- Since C is on the major arc AB, ?ACB is less than 90°.

- If you’re given ?BAQ = 58°, then ?ACB = 58° as well.

- The angle at the center, ?AOB, is twice the angle subtended at the circumference, so ?AOB = 2 × ?ACB = 2 × 58° = 116°.

So, the answer is:

- Option 1: 98 — doesn’t fit.

- Option 2: 112 — nope.

- Option 3: 110 — also not it.

- Option 4: 116 — this is right.

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