2020 AMC 10A Problems/Problem 20
Contents
Problem
Quadrilateral satisfies
and
Diagonals
and
intersect at point
and
What is the area of quadrilateral
Solution
It's crucial to draw a good diagram for this one. Since and
, we get
. Now we need to find
to get the area of the whole quadrilateral. Drop an altitude from
to
and call the point of intersection
. Let
. Since
, then
. By dropping this altitude, we can also see two similar triangles,
and
. Since
is
, and
, we get that
. Now, if we redraw another diagram just of
, we get that
. Now expanding, simplifying, and dividing by the GCF, we get
. This factors to
. Since lengths cannot be negative,
. Since
,
. So
(I'm very sorry if you're a visual learner - Ultraman)
Video Solution
~IceMatrix
See Also
2020 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by Problem 19 |
Followed by Problem 21 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AMC 10 Problems and Solutions |
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