Multiple choice

In a circle with center O, AB is a diameter and CD is a chord such that ∠ABC = 34° and CD = BD. What is the measure of ∠DBC?

  1. 32°

  2. 30°

  3. 24°

  4. 28°
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D Correct answer
Explanation

AB is diameter, so ∠ACB = 90° (angle in semicircle). Given ∠ABC = 34°, so ∠CAB = 56°. Since CD = BD, triangle CBD is isosceles with base CD. In the circle configuration, ∠DBC = 28° by angle chasing in cyclic quadrilateral and using properties of equal chords.

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