AB is a diameter of a circle with center O. A tangent is drawn at point A. C is a point on the circle such that BC produced meets the tangent at P. If ∠APC = 62º, then find the measure of the minor arc AC(i.e.∠ ABC).

This question was previously asked in
SSC CGL 2021 Tier-I (Held On : 11 April 2022 Shift 1)
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  1. 31º
  2. 62º
  3. 28º
  4. 66º

Answer (Detailed Solution Below)

Option 3 : 28º
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Detailed Solution

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Given:

AB is a diameter of a circle with a center O

∠APC = 62º

Concept used:

The radius/diameter of a circle is always perpendicular to the tangent line.

Sum of all three angles of a triangle = 180°

Calculation:

 F1 Savita SSC 4-10-22 D1

Minor arc AC will create angle CBA

∠APC = 62º = ∠APB

∠BAP = 90° (diameter perpendicular to tangent)

In Δ APB,

∠APB + ∠BAP + PBA = 180° 

⇒ PBA = 180° - (90° + 62°)

⇒ PBA = 28° 

∴ The measure of minor arc AC is 28° 

Mistake PointsMeasure of the minor arc AC is asked,

∠ABC marks arc AC, 

∴ ∠ABC is the correct angle to show a measure of arc AC

This is a previous year's question, and according to the commission, this is the correct answer.

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