Two tangents are drawn from an external point P to a circle. If the angle between the two tangents is 50°, what is the angle subtended by the minor arc at the centre?

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Question

Two tangents are drawn from an external point P to a circle. If the angle between the two tangents is 50°, what is the angle subtended by the minor arc at the centre?

Accepted Answer

130° — The angle between two tangents from an external point and the central angle of the minor arc are supplementary: angle at centre (minor) = 180° − (50° ÷ 2) × 2. Using the theorem: angle between tangents = 180° − central angle of minor arc, so central angle = 180° − 50° = 130°. Option A repeats the given angle. Option B halves it incorrectly. Option D gives the major arc angle (360° − 130° = 230°), which students sometimes select instead.

Answer

50°

Answer

130°

Answer

100°

Answer

230°

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