2016 AMC 8 Problems/Problem 23
Contents
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
.
Video Solution 1
https://youtu.be/UZqVG5Q1liA?si=LDc8tMTnj1FMMlZc
Video Solution 2
Video Solution 3
https://youtu.be/FDgcLW4frg8?t=968
Video Solution 4
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 |
These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions.