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A chord of a circle is equal to the radius of the circle. Find

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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.

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Text solutionVerified

Consider the figure.

Given,

A B

is equal to the radius of the circle.

△ O A B

O A = OB = A B =

radius of the circle.

Thus,

△ O A B

is an equilateral triangle.

and

∠ A OC = 60°

Also,

∠ A CB = \frac{1}{2} ∠ A OB = \frac{1}{2} \times 60° = 30°

Since,

A CB D

is a cyclic quadrilateral,

∠ A CB + ∠ A D B = 180°

....[Opposite angles of cyclic quadrilateral are supplementary]

\Rightarrow ∠ A D B = 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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Question Text	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 Type	Text solution:1
Upvotes	150

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.

Text solutionVerified

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