# inscribe angle

## Quadrilateral with one side as diameter of circumscribing circle

**Problem PG-010**

The quadrilateral ABCD shown in Fig. PG-010 is inscribed in a circle with side AD coinciding with the diameter of the circle. if sides AB, BC, and CD are 8 cm, 10 cm, and 12 cm long, respectively, find the radius of the circumscribing circle.

## Area of Regular Six-Pointed Star

**Problem**

Find the area of the regular six-pointed star inscribed in a circle of radius 20 cm.

## Area of Regular Five-Pointed Star

**Problem**

Find the area of the regular five-pointed star inscribed in a circle of radius 20 cm.

## Relationship Between Central Angle and Inscribed Angle

Central angle = Angle subtended by an arc of the circle from the center of the circle.

Inscribed angle = Angle subtended by an arc of the circle from any point on the circumference of the circle. Also called *circumferential angle* and *peripheral angle*.

Figure below shows a central angle and inscribed angle intercepting the same arc AB. The relationship between the two is given by

if and only if both angles intercepted the same arc. In the figure below, θ and α intercepted the same arc AB.