Question

a chord of a circle is equal to the radius of a Circle. Find the angle subtended by the chord at a point on minor arc and major arc​

Answer 1

here is the answer with full explanation....

Step-by-step explanation:

Consider the figure.

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.

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.

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