CDS 2026 (I) Elementary Mathematics, question 52

Topic: Geometry

Answers by SolvedPaper. UPSC has not released the official answer key for this paper yet. We will update it when they do.

Q52

Let O be the centre of a circle. Let A, B and C lie on the circle such that ∠ABC=153∘\angle ABC=153^{\circ}. What is the value of ∠AOC\angle AOC ?

  1. (a) 54∘54^{\circ}Correct answer
  2. (b) 52∘52^{\circ}
  3. (c) 39∘39^{\circ}
  4. (d) 27∘27^{\circ}

Solution.

Answer: (a) 54∘54^{\circ}

  1. The angle at B intercepts the arc AC not containing B.
  2. That arc measures 2×153∘=306∘2 \times 153^{\circ} = 306^{\circ}, so the remaining minor arc AC measures 360∘−306∘=54∘360^{\circ} - 306^{\circ} = 54^{\circ}.
  3. The smaller central angle AOC is therefore 54°.
  4. The reflex central angle would be 306°.