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A triangle ABC is inscribed in a circle with centre O, and the angle at A is 60 degrees. From O a perpendicular OD is dropped onto the chord BC. Find the measure of angle BOD.

1. 30 deg
2. 45 deg
3. 60 deg
4. 90 deg

Correct answer: 60 deg

Solution

The central angle BOC = 2 * angle A = 2 * 60 = 120 degrees (angle at centre is twice the angle at the circumference on the same arc). Since OD is perpendicular to chord BC, it bisects angle BOC, so angle BOD = 120/2 = 60 degrees.

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