Multiple choice

In a circle of center O, AB is a diameter and CD is a chord to the circle. ∠AOD = 106o then what is the value of ∠BCD.

  1. 35°

  2. 75°

  3. 40°

  4. 37°
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

In a circle, if AB is a diameter, then any angle subtended by AB in the opposite semicircle is a right angle. So angle ACB = 90°. Triangle AOD is isosceles (OA = OD as radii). Given angle AOD = 106°, so angles OAD = ODA = (180 - 106)/2 = 37° each. Angle BCD = angle ODA = 37° (same angle).

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