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A chord of a circle is equal to the radius of the circle. Find the angle subtended by the chord at a point on the major arc? |
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Answer» Consider the figure.Given,AB is EQUAL to the radius of the circle.In △OAB,OA=OB=AB= radius of the circle.Thus, △OAB is an equilateral triangle.and ∠AOC=60°.ALSO, ∠ACB= 21 ∠AOB= 21 ×60°=30°.Since, ACBD is a cyclic quadrilateral,∠ACB+∠ADB=180° ....[Opposite ANGLES of cyclic quadrilateral are supplementary]⇒∠ADB=180°−30°=150°.Thus, angle subtend by the chord at a point on the minor arc and also at a point on the major arc are 150° and 30°, RESPECTIVELY. |
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