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Omni-MATH / Let ABC be an acute triangle with orthocenter H. Let D,E be the feet of the A,B-altitudes respectively. Given that AH=20 and HD=15 and BE=56, find the length of BH.

Problem

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problem

Let ABCA B C be an acute triangle with orthocenter HH. Let D,ED, E be the feet of the A,BA, B-altitudes respectively. Given that AH=20A H=20 and HD=15H D=15 and BE=56B E=56, find the length of BHB H.
Plain-text mathematical notation (without MathML)
Let ABC be an acute triangle with orthocenter H. Let D,E be the feet of the A,B-altitudes respectively. Given that AH=20 and HD=15 and BE=56, find the length of BH.
Original LaTeX notation
Let $A B C$ be an acute triangle with orthocenter $H$. Let $D, E$ be the feet of the $A, B$-altitudes respectively. Given that $A H=20$ and $H D=15$ and $B E=56$, find the length of $B H$.

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Source and history

task_id
5c899d1a-6264-526b-ad91-f39bb6a30d69
task_key
test--5c899d1a-6264-526b-ad91-f39bb6a30d69
task_revision_id
1
config / split
/ test

Official source

initial import