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jmc

geometry junior

Problem

Two congruent circles centered at points and each pass through the other circle's center. The line containing both and is extended to intersect the circles at points and . The circles intersect at two points, one of which is . What is the degree measure of ?
(A)
(B)
(C)
(D)
Solution
Observe that is equilateral. Therefore, . Since is a straight line, we conclude that . Since (both are radii of the same circle), is isosceles, meaning that . Similarly, . Now, . Therefore, the answer is .
Final answer
C