Difference between revisions of "2021 AMC 10B Problems/Problem 21"
Pi is 3.14 (talk | contribs) (→Video Solution by OmegaLearn (Logarithmic Tricks)) |
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label("D",D,NE); | label("D",D,NE); | ||
label("E",E,NW); | label("E",E,NW); | ||
− | label("C",CC,N); | + | label("C'",CC,N); |
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==Solution (Outlined)== | ==Solution (Outlined)== | ||
double angle tangent to find angle ACE | double angle tangent to find angle ACE |
Revision as of 21:51, 11 February 2021
Contents
[hide]Problem
A square piece of paper has side length and vertices and in that order. As shown in the figure, the paper is folded so that vertex meets edge at point , and edge at point . Suppose that . What is the perimeter of triangle
Solution (Outlined)
double angle tangent to find angle ACE then trig
Solution (Quicksolve)
Assume that E is the midpoint of . Then, and since , . By the Pythagorean Theorem, . It easily follows that our desired perimeter is ~samrocksnature
Video Solution by OmegaLearn (Using Pythagoras Theorem and Similar Triangles)
~ pi_is_3.14