ORCLES2. A chord of a circle is equal to the radius of thecircle. Find the angle subtended by the chord ata point on the minor arc and also at a point on themajor arc.O and R ae

ORCLES2. A chord of a circle is equal to the radius of thecircle. Find

1.	ORCLES2. A chord of a circle is equal to the radius of thecircle. Find the angle subtended by the chord ata point on the minor arc and also at a point on themajor arc.O and R ae
Answer» In ΔOAB,AB = OA = OB (radii)Hence ΔOAB is an equilateral triangleThat is each angle of ΔOAB is 60°∴ ∠AOB = 60°∠AOB = 2∠ACB [Angle subtended by an arc of a circle at the centre is double the angle subtended by it on any part of the circle]Hence∠ACB = 30°In cyclic quadrilateral ADBC∠ADB +∠ACB = 180° (Sum of opposite angles in cyclic quadrilateral is 180°)⇒ ∠ADB = 180° − 30° = 150°Therefore, angle subtended by the chord at a point on the major arc and the minor arc are 30° and 150° respectively.