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Omni-MATH / Let ABC be an acute isosceles triangle with orthocenter H. Let M and N be the midpoints of sides (AB)¯ and (AC)¯, respectively. The circumcircle of triangle MHN intersects line BC …

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problem

Let ABCA B C be an acute isosceles triangle with orthocenter HH. Let MM and NN be the midpoints of sides AB¯\overline{A B} and AC¯\overline{A C}, respectively. The circumcircle of triangle MHNM H N intersects line BCB C at two points XX and YY. Given XY=AB=AC=2X Y=A B=A C=2, compute BC2B C^{2}.
Plain-text mathematical notation (without MathML)
Let ABC be an acute isosceles triangle with orthocenter H. Let M and N be the midpoints of sides (AB)¯ and (AC)¯, respectively. The circumcircle of triangle MHN intersects line BC at two points X and Y. Given XY=AB=AC=2, compute BC².
Original LaTeX notation
Let $A B C$ be an acute isosceles triangle with orthocenter $H$. Let $M$ and $N$ be the midpoints of sides $\overline{A B}$ and $\overline{A C}$, respectively. The circumcircle of triangle $M H N$ intersects line $B C$ at two points $X$ and $Y$. Given $X Y=A B=A C=2$, compute $B C^{2}$.

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Source and history

task_id
5101283c-0ce1-5a00-820e-12fff750d4c2
task_key
test--5101283c-0ce1-5a00-820e-12fff750d4c2
task_revision_id
1
config / split
/ test

Official source

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