2020 CIME I Problems/Problem 5
Problem 5
Let be a rectangle with sides
and let
be the reflection of
over
. If
and the area of
is
, find the area of
.
Solution
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Let be the center of rectangle
. Because
is the reflection of
over
and
degrees, we have
degrees. This means
lies on the circle with diameter
, or the circumcircle of rectangle
. We are given
, so by symmetry,
. Since the three lengths are equal and
degrees, we must have
degrees, so
,
,
are all equilateral. Given that the area of cyclic quadrilateral
is
, the area of
is
. This is
of the area of rectangle
, so the answer is
.
See also
2020 CIME I (Problems • Answer Key • Resources) | ||
Preceded by Problem 4 |
Followed by Problem 6 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
All CIME Problems and Solutions |
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