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​

Answer 1

Step-by-step explanation:

let the cord be AB

OB equals OA equals AB

hence it is an equilateral triangle

angle AOB equals 60

therefore angle formed on minor arc is 60

angle formed on major arc is 360-60 = 300

Answer 2

$\huge\fbox\red{✧Solution :}$

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°.

Also, ∠ACB = 1/2 ∠AOB = 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.