In a circle with center O, AB is the dia

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Target Exam

CUET

Subject

General Test

Chapter

Quantitative Reasoning

Topic

Geometry

Question:

In a circle with center O, AB is the diameter and CD is a chord such that ABCD is a trapezium. If ∠BAC = 30°, then ∠CAD is equal to?

Options:

120°

30°

60°

110°

Correct Answer:

30°

Explanation:

In ΔACB

∠ACB = 90° (angle in semicircle)

∠ABC = 90° - 30° = 60°

∠ADC = 120° (cyclic quad.)

∠DCA = ∠CAB = 30° (alternate angle)

∠CAD = 180° - (120° + 30°) = 30°