**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 **