A geometry problem by Gurjot Sodhi

Geometry Level 2

In the given fig. ED is parallel to diameter AC of a circle with center O. If ∠CBE = 64°, determine ∠CED.

25° 26° 64° 32°

1 solution

Marta Reece
Apr 14, 2017

$\angle EBC=64^\circ=>\angle EOC=2\times 64^\circ=128^\circ.$

$\triangle EOC$ is isosceles, therefore $\angle OCE=\angle OEC=\frac{1}{2}(180^\circ-128^\circ)=26^\circ$

$AC||ED=>\angle CED=\angle OCE=26^\circ$