A chord of a circle is equal to the radius of the circle. Find the angle subtended by the chord ata point on the minor arc and also at a point on the major arc.

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In ΔOAB, AB = OA = OB = radius ∴ ΔOAB is an equilateral triangle. Therefore, each interior angle of this triangle will be of 60°. ∴ ∠AOB = 60° In cyclic quadrilateral ACBD, ∠ACB + ∠ADB = 180° (Opposite angle in cyclic quadrilateral) ⇒ ∠ADB...
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In ΔOAB, AB = OA = OB = radius ∴ ΔOAB is an equilateral triangle. Therefore, each interior angle of this triangle will be of 60°. ∴ ∠AOB = 60° In cyclic quadrilateral ACBD, ∠ACB + ∠ADB = 180° (Opposite angle in cyclic quadrilateral) ⇒ ∠ADB = 180° − 30° = 150° Therefore, angle subtended by this chord at a point on the major arc and the minor arc are 30° and 150° respectively. read less
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