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 and Explanation
In ∆OAB,
AB = OA = OB = radius
∠∆OAB is an equilateral triangle.
Therefore, each interior angle of this triangle will be of 60°.
∠AOB = 60°
∠ACB=\(\frac{1}{2}\)∠AOB=\(\frac{1}{2}\)(60°)=30°
In cyclic quadrilateral ACBD,
∠ACB + ∠ADB = 180° (Opposite angle in cyclic quadrilateral)
∠ADB = 180° − 30° = 150°
Therefore, angle subtended by this chord at a point on the major arc and the minor arc are 30° and 150° respectively.
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