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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 minor arc and also at a point on the major arc.

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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 minor arc and also at a point on the major arc.

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Here, the chord AB is equal to the radius of the circle. In the above diagram, OA and OB are the two radii of the circle.

Now, consider the ΔOAB.

AB = OA = OB = radius of the circle.

So, it can be said that ΔOAB has all equal sides and thus, it is an equilateral triangle.

∴ AOC = 60°

And, ACB = \(\frac{1}{2}\) AOB

ACB = \(\frac{1}{2}\) × 60° = 30°

Now, since ACBD is a cyclic quadrilateral,

ADB + ACB = 180° (Since they are the opposite angles of a cyclic quadrilateral)

ADB = 180°-30° = 150°

So, the angle subtended 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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