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.
Solution:
Let’s suppose that we have chord PQ equal to the radius of the given circle. So, we have
which means that
is equilateral.
Let A be any point on the minor arc and B be any point on the major arc.
(Angle subtended by an arc at the centre is double the angle subtended by it at the circumference of the circle.)
We can note that quadrilateral PAQB is cyclic.
(Sum of opposite angles of a cyclic quadrilateral is equal to
)
Therefore, angle subtended by the chord at minor arc
And, angle subtended by the chord at major arc
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