intersecting chords

Area Bounded by Intersecting Chords in a Circle

Problem
Chords AB and CD intersect each other at E inside the circle. AE = 8 cm, CE = 12 cm, and DE = 20 cm. If AB is the diameter of the circle, compute the area of AEC.

A.   61.04 cm2 C.   39.84 cm2
B.   52.05 cm2 D.   48.62 cm2

 

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
 

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

 

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

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