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# Question 1

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.

• Solution

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

Now, consider the ΔOAB. Here,

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 = 1/2 ∠AOB

So, ∠ACB = 1/2 × 60° = 30°

Now, since ACBD is a cyclic quadrilateral,

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

So, ∠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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