Question

A chord of a circle is equal to the radius of circle find the angle subtended by the chord at a point on the minor arc and also at a point on the major arc​

Answer 1

Answer:

whe a chord is equal to the radius, it forms an equilateral triangle with the centre.

so it subtends 60° at the centre.

therefore it subtends 60°/2 = 30° at any point on the major arc and 180° - 30° = 150° on the minor arc [ angle on major arc and Minor arc form a linear pair as it is cyclic ]

Answer 2

Answer:

Given,

AB is equal to the radius of the circle.

In △OAB,

OA=OB=AB= radius of the circle.

Thus, △OAB is an equilateral triangle.

∠AOC=60°

Also, ∠ACB= 1/2 ∠AOB= 1/2 ×60°=30°

ACBD is a cyclic quadrilateral,

∠ACB+∠ADB=180° ∣ Opposite angles of cyclic quadrilateral

⇒∠ADB=180°−30°=150°

Thus, angle subtend by the chord at a point on the minor arc and also at a point on the major arc are 150° and 30° respectively.

hope this helps you.

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