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Omni-MATH / P is a point inside triangle ABC, and lines AP,BP,CP intersect the opposite sides BC,CA,AB in points D,E,F, respectively. It is given that ∠APB=90^(∘), and that AC=BC and AB=BD. We…

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problem

PP is a point inside triangle ABCA B C, and lines AP,BP,CPA P, B P, C P intersect the opposite sides BC,CA,ABB C, C A, A B in points D,E,FD, E, F, respectively. It is given that ∠APB=90∘\angle A P B=90^{\circ}, and that AC=BCA C=B C and AB=BDA B=B D. We also know that BF=1B F=1, and that BC=999B C=999. Find AFA F.
Plain-text mathematical notation (without MathML)
P is a point inside triangle ABC, and lines AP,BP,CP intersect the opposite sides BC,CA,AB in points D,E,F, respectively. It is given that ∠APB=90^(∘), and that AC=BC and AB=BD. We also know that BF=1, and that BC=999. Find AF.
Original LaTeX notation
$P$ is a point inside triangle $A B C$, and lines $A P, B P, C P$ intersect the opposite sides $B C, C A, A B$ in points $D, E, F$, respectively. It is given that $\angle A P B=90^{\circ}$, and that $A C=B C$ and $A B=B D$. We also know that $B F=1$, and that $B C=999$. Find $A F$.

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task_id
a77e5a22-6bcb-51b5-892a-89c6082da518
task_key
test--a77e5a22-6bcb-51b5-892a-89c6082da518
task_revision_id
1
config / split
/ test

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