Question

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


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Answer 1

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.

and ∠AOC=60°.

Also, ∠ACB=

2

1

∠AOB=

2

1

×60°=30°.

Since, ACBD is a cyclic quadrilateral,

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

⇒∠ADB=180°−30°=150°.

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