## Angle between two chords

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**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.

**Problem**

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

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**Problem**

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

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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

$\alpha = 2\theta \, \text{ or } \, \theta = \frac{1}{2}\alpha$

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