2021 AMC 12B Problems/Problem 11
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Problem 11
Triangle 
has 
and 
. Let 
be the point on 
such that 
. There are exactly two points 
and 
on line 
such that quadrilaterals 
and 
are trapezoids. What is the distance 
Solutions
Solution 1
Using Stewart's Theorem of 
calculate the cevian to be 
. It then follows that the answer must also have a factor of the 
. Having eliminated 3 answer choices, we then proceed to draw a rudimentary somewhat accurate diagram of this figure. Drawing that, we realize that 
is too small making out answer 
