Multiple choice

A triangle ABC is inscribed in a circle with centre O. AO is produced to meet the circle at K and AD ⊥ BC. If ∠B = 800 and ∠C = 640, then the measure of ∠DAK is :

  1. 10°

  2. 16°

  3. 12°

  4. 20°
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

In triangle ABC, ∠A = 180° - 80° - 64° = 36°. Since AK is diameter, ∠ABK = 90° and ∠BKA = ∠BCA = 64° (same segment). So ∠BAK = 90° - 64° = 26°. AD is altitude, so ∠BAD = 90° - 80° = 10°. Thus ∠DAK = ∠BAK - ∠BAD = 26° - 10° = 16°.

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