Question

Two congruent circles centered at points $A$ and $B$ each pass through the other circle's center. The line containing both $A$ and $B$ is extended to intersect the circles at points $C$ and $D.$

The circles intersect at two points, one of which is $E.$ What is the degree measure of $\angle CED?$

$90$

$105$

$120$

$135$

$150$

Video solution:

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Written solution:

We know that $AE = EB = AB$ since they are all radii of congruent circles, so they form an equilateral triangle, which means that $\angle AEB = 60^{\circ}.$

Also, since $\overline{DB}$ and $\overline{AC}$ are diameters, $\angle DEB = \angle AEC = 90^{\circ}.$ Therefore, $\begin{align*}\angle CED = \angle DEB &+ \angle AEC\\ &- \angle AEB,\end{align*}$ which equals $120^{\circ}.$

Thus, C is the correct answer.

2016 AMC 8 Problem 23

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Written solution:

Problem 23 in Other Years