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

The chord AB is equal to the radius of the circle. 

OA and OB are the two radii of the circle.

From ΔOAB. 

AB = OA = OB = radius of the circle.

 ΔOAB is an equilateral triangle.

∴ AOC = 60°

And, ACB = ½ AOB

So, ACB = ½ × 60° = 30°

Now, 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 is 150° and 30° respectively.

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