Difference between revisions of "2016 AMC 8 Problems/Problem 23"
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https://youtu.be/NumhAGApJ7c - Happytwin | https://youtu.be/NumhAGApJ7c - Happytwin | ||
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+ | == Video Solution == | ||
+ | https://youtu.be/FDgcLW4frg8?t=968 | ||
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+ | ~ pi_is_3.14 | ||
==See Also== | ==See Also== | ||
{{AMC8 box|year=2016|num-b=22|num-a=24}} | {{AMC8 box|year=2016|num-b=22|num-a=24}} | ||
{{MAA Notice}} | {{MAA Notice}} |
Revision as of 03:50, 28 January 2021
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 ?
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
Video Solution
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.