Multiple choice

In a circle with centre O, AB is the diameter and CD is a chord such that ABCD is a trapezium. If (\angle BAC = 24^{\circ}), then (\angle CAD) is equal to:

  1. 48

  2. 36

  3. 42

  4. 24
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

In a cyclic trapezium, opposite angles sum to 180°, so ∠DAB + ∠BCD = 180°. Since AB is diameter, ∠ACB = 90°. Given ∠BAC = 24°, then ∠BCD = 90°-24° = 66°. So ∠DAB = 114°, meaning ∠CAD = 114°-24° = 90°-66° = 42° in triangle ACD. Option D (24°) merely repeats ∠BAC.

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