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}} |
Latest revision as of 04:50, 28 January 2021
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 .
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.