2016 AMC 8 Problems/Problem 23
Contents
[hide]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
?
Solution
Observe that is equilateral (all are radii of congruent circles). 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
.
Video Solution by Elijahman
https://youtu.be/UZqVG5Q1liA?si=LDc8tMTnj1FMMlZc
~Elijahman
Video Solution by Education, The Study of Everything
Video Solution by Omega Learn
https://youtu.be/FDgcLW4frg8?t=968
~ pi_is_3.14
Video Solution by WhyMath
~savannahsolver
See Also
2016 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 22 |
Followed by Problem 24 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AJHSME/AMC 8 Problems and Solutions |
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