Question

The center of the circle lies ……… .
In the minor region
On the major arc
In the major region​

Answer 1

Here the figure

solution -

Here, the chord AB is equal to the radius of the circle. In the above diagram, OA and OB are the two radii of the circle.

Now, consider the ΔOAB. Here,

AB = OA = OB = radius of the circle.

So, it can be said that ΔOAB has all equal sides and thus, it is an equilateral triangle.

∴ AOC = 60°

And, ACB = ½ AOB( central angle) or 10.8 therein)

So, ACB = ½ × 60° = 30°

Now, since ACBD is a cyclic quadrilateral,

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

So, ADB = 180°-30° = 150°

So, the angle subtended by the chord at a point on the minor arc and also at a point on the major arc are 150° and 30° respectively