2018 AMC 12A Problems/Problem 23
Problem
In and Points and lie on sides and respectively, so that Let and be the midpoints of segments and respectively. What is the degree measure of the acute angle formed by lines and
Solution
Let be the origin, and lie on the x axis.
We can find and
Then, we have and
Notice that the tangent of our desired points is the the absolute difference between the y coordinates of the two points divided by the absolute difference between the x coordinates of the two points.
This evaluates to Now, using sum to product identities, we have this equal to so the answer is (lifeisgood03)
See Also
2018 AMC 12A (Problems • Answer Key • Resources) | |
Preceded by Problem 22 |
Followed by Problem 24 |
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All AMC 12 Problems and Solutions |
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