Multiple choice

AB and CD are two chords in a circle with centre O and AD is a diameter. AB and CD produced meet at a point P outside the circle. If ∠ APD = 250 and ∠ DAP = 390, then the measure of ∠CBD is:

  1. 290

  2. 280

  3. 440

  4. 260
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

In ΔAPD: ∠APD + ∠DAP + ∠ADP = 180°, so 25° + 39° + ∠ADP = 180°, giving ∠ADP = 116°. Since AD is a diameter, ∠ABD = 90° (angle in semicircle). ∠CBD = ∠ABD - ∠ABC. Using cyclic quadrilateral ABCD: ∠ABC = 180° - ∠ADC = 180° - 116° = 64°. Therefore ∠CBD = 90° - 64° = 26°. Options A (29°), B (28°), and C (44°) are incorrect.

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