Difference between revisions of "Talk:2013 AMC 12B Problems/Problem 25"
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Given a trapezoid with bases <math>AB</math> and <math>CD</math>, there exists a point <math>E</math> on <math>CD</math> such that drawing the segments <math>AE</math> and <math>BE</math> partitions the trapezoid into <math>3</math> similar isosceles triangles, each with long side twice the short side. What is the sum of all possible values of <math>\frac{CD}{AB}</math>?The answer is in the form �rac{m}{n}, where gcd(m, n) = 1. Please provide the value of m + n. | Given a trapezoid with bases <math>AB</math> and <math>CD</math>, there exists a point <math>E</math> on <math>CD</math> such that drawing the segments <math>AE</math> and <math>BE</math> partitions the trapezoid into <math>3</math> similar isosceles triangles, each with long side twice the short side. What is the sum of all possible values of <math>\frac{CD}{AB}</math>?The answer is in the form �rac{m}{n}, where gcd(m, n) = 1. Please provide the value of m + n. | ||
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Latest revision as of 19:39, 1 May 2025
Given a trapezoid with bases 
and 
, there exists a point 
on such that drawing the segments 
and 
partitions the trapezoid into 
similar isosceles triangles, each with long side twice the short side. What is the sum of all possible values of 
?The answer is in the form �rac{m}{n}, where gcd(m, n) = 1. Please provide the value of m + n.
