Question

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 1

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Answer 2

*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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