Question

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 1

The chord $AB$is equal to the radius of the circle.

$OA$and $OB$are the two radii of the circle.

From $\Delta OAB$.

$AB=OA=OB=$ radius of the circle.

$\Delta OAB$is an equilateral triangle.

$\therefore AOC=60°$

And,$\angle ACB=\frac{1}{2}\angle AOB$

So, $\angle ACB=\frac{1}{2}\times 60°=30°$

Now, $ACBD$is a cyclic quadrilateral,

$\angle ADB+\angle ACB=180°$(Since they are the opposite angles of a cyclic quadrilateral)

So, $\angle ADB=180°-30°=150°$

Hence, the angle subtended by the chord at a point on the minor arc and also at a point on the major arc is $150°\&30°$ respectively.