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Question
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
In ΔOAB,
AB = OA = OB = radius
∴ ΔOAB is an equilateral triangle.
Therefore, each interior angle of this triangle will be of 60°.
∴ ∠AOB = 60°
∠ACB = `1/2angleAOB`
∠ACB = `1/2(60^@)`
∠ACB = 30°
In cyclic quadrilateral ACBD,
∠ACB + ∠ADB = 180° ...(Opposite angle in cyclic quadrilateral)
⇒ ∠ADB = 180° − 30° = 150°
Therefore, the angles subtended by this chord at a point on the major arc and the minor arc are 30° and 150° respectively.
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