Question

a chord of a circle is equal to the radius.find the angle substended by the chord at a point on the minor arc​

Answer 1

AB is equal to the radius of the circle.

In △OAB,

OA=OB=AB= radius of the circle.

Thus, △OAB is an equilateral triangle.

and ∠AOC=60°.

$∠ACB= \frac{1}{2} ∠AOB \\ = \frac{1}{2} ×60°=30°$

Since, ACBD is a cyclic quadrilateral,

∠ACB+∠ADB=180° --------[Opposite angles of cyclic quadrilateral are supplementary]

⇒∠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.