CAT 1995 — QA Question 27
Basics of CirclesEasy
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
Correct answer: 40°
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°.