A chord subtends an angle of 100° at the center of a circle. What is the angle subtended by the chord in the major segment of the circle?
Explanation:
The angle subtended by a chord on a point on the circumference (which lies in the major segment) of the circle measures half the angle subtended by the same chord at the center.
In the above figure, chord AC subtends an angle ∠ADB at point D lying on the major arc and an angle ∠AOB at the center of the circle.
∴ m ∠AOB = 2 × m ∠ADB
m ∠AOB = 100°
∴ m ∠ADB = 50°
∴ The angle subtended by the chord AB in the major segment = 50°
Hence, option (c).
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