2021 AIME I Problems/Problem 11

Problem

Let $ABCD$ be a cyclic quadrilateral with $AB=4,BC=5,CD=6,$ and $DA=7$ . Let $A_1$ and $C_1$ be the feet of the perpendiculars from $A$ and $C$ , respectively, to line $BD,$ and let $B_1$ and $D_1$ be the feet of the perpendiculars from $B$ and $D,$ respectively, to line $AC$ . The perimeter of $A_1B_1C_1D_1$ is $\frac mn$ , where $m$ and $n$ are relatively prime positive integers. Find $m+n$ .

2021 AIME I (Problems • Answer Key • Resources)
Preceded by Problem 10	Followed by Problem 12
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15
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2021 AIME I Problems/Problem 11

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