2021 AMC 12B Problems/Problem 11
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 semiaccurate diagram of this figure. Drawing that, we realize that
is too small making out answer
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