A chord is a circle is equal to the radius of the circle . Find the angle substended by the chord at a point on the major arc?
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A chord is a circle is equal to the radius of the circle . Find the angle substended by the chord at a point on the major arc?
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*Question:
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A chord is a circle is equal to the radius of the circle . Find the angle substended by the chord at a point on the major arc?
*Answer:
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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.
∠AOC = 60°
Also, ∠ACB= 1/2 ∠AOB= 1/2 × 60° = 30°
∠ACB+∠ADB=180° {Opposite angles of cyclic quadrilateral}
⇒∠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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