Difference between revisions of "2016 AMC 8 Problems/Problem 23"
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Revision as of 15:52, 28 December 2021
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
?
Solutions
Solution 1
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
.
Solution 2
We know that is equilateral, because all of its sides are congruent radii. Because point
is the center of a circle,
is at the border of a circle, and
and
are points on the edge of that circle,
. Since
is isosceles, angle
degrees -SweetMango77.
Video Solution
https://youtu.be/NumhAGApJ7c - Happytwin
https://youtu.be/FDgcLW4frg8?t=968
~ pi_is_3.14
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 |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.