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CAT 1995 — QA Question 27

Basics of CirclesEasy
Passage / Data

Direction: Answer the questions based on the following information.
Four sisters — Suvarna, Tara, Uma and Vibha are playing a game such that the loser doubles the money of each of the other players from her share. They played four games and each sister lost one game in alphabetical order. At the end of fourth game, each sister had Rs.32.

In the given figure, AB is diameter of the circle and points C and D are on the circumference such that ∠CAD = 30° and ∠CBA = 70°. What is the measure of ∠ACD?

Answer & solution

  • 40°

  • B

    50°

  • C

    30°

  • D

    90°

Solution

If we draw the imaginary lines AC and BD, we find that
∠ CAD and ∠CBD are subtended by the same chord DC.
∴ ∠CAD = ∠CBD = 30°.
Thus, ∠DBA = (70 – 30) = 40°.
Also, ∠DBA and ∠ACD are subtended by the same chord DA.
Hence, ∠ACD = DBA = ∠40°.

CAT 1995 QA Q27: In the given figure, AB is diameter of the circle and points C and D are on the circumference such that ∠C — Solution | TheCATExam