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 $\angle CED?$

$90$

$105$

$120$

$135$

$150$

Answer: C

Concepts:equilateral triangle inscribed angle angle chasing

Difficulty rating: 1510

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 $\angle AEB = 60^{\circ}.$

The segments $\overline{DB}$ and $\overline{AC}$ are diameters, so $\angle DEB=\angle AEC=90^\circ.$ Therefore, $\begin{aligned} \angle CED &= \angle DEB+\angle AEC\\ &\qquad-\angle AEB\\ &=90^\circ+90^\circ-60^\circ\\ &=120^\circ. \end{aligned}$

Thus, C is the correct answer.

2016 AMC 8 Problem 23

Answer: C

Difficulty rating: 1510

Video solution:

Written solution:

Problem 23 in Other Years