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Omni-MATH / Let ABC be an acute triangle with circumcenter O such that AB=4,AC=5, and BC=6. Let D be the foot of the altitude from A to BC, and E be the intersection of AO with BC. Suppose tha…

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problem

Let ABCA B C be an acute triangle with circumcenter OO such that AB=4,AC=5A B=4, A C=5, and BC=6B C=6. Let DD be the foot of the altitude from AA to BCB C, and EE be the intersection of AOA O with BCB C. Suppose that XX is on BCB C between DD and EE such that there is a point YY on ADA D satisfying XY∥AOX Y \parallel A O and YO⊥AXY O \perp A X. Determine the length of BXB X.
Plain-text mathematical notation (without MathML)
Let ABC be an acute triangle with circumcenter O such that AB=4,AC=5, and BC=6. Let D be the foot of the altitude from A to BC, and E be the intersection of AO with BC. Suppose that X is on BC between D and E such that there is a point Y on AD satisfying XY∥AO and YO⊥AX. Determine the length of BX.
Original LaTeX notation
Let \(A B C\) be an acute triangle with circumcenter \(O\) such that \(A B=4, A C=5\), and \(B C=6\). Let \(D\) be the foot of the altitude from \(A\) to \(B C\), and \(E\) be the intersection of \(A O\) with \(B C\). Suppose that \(X\) is on \(B C\) between \(D\) and \(E\) such that there is a point \(Y\) on \(A D\) satisfying \(X Y \parallel A O\) and \(Y O \perp A X\). Determine the length of \(B X\).

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task_id
9ba7e5d7-444b-58f8-8ca7-8f32d368deec
task_key
test--9ba7e5d7-444b-58f8-8ca7-8f32d368deec
task_revision_id
1
config / split
/ test

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