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

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

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Solution:

A chord of a circle is equal to the radius of the circle. The angle subtended by the chords at a point on the minor arc and also at a point on the major arc is 30o.
It is given that chord of a circle is equal to its radius.
Let O be the centre of the circle, OA be the radius and AB be the chord, as shown in the figure.
The angle subtended by the chords at a point on the minor arc and also at a point on the major arc is 30o.
In ∆AOB,
So, ∆AOB is an equilateral triangle.

By degree measure theorem,

Opposite angles of cyclic quadrilateral are supplementary.

Therefore, angle by chord AB at minor arc = 150°.
Angle by chord AB at major arc = 30°.
Hence, the required answer is 30o.

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