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Omni-MATH / Let ABC be a triangle with AB=4,BC=8, and CA=5. Let M be the midpoint of BC, and let D be the point on the circumcircle of ABC so that segment AD intersects the interior of ABC, an…

Problem

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problem

Let ABCA B C be a triangle with AB=4,BC=8A B=4, B C=8, and CA=5C A=5. Let MM be the midpoint of BCB C, and let DD be the point on the circumcircle of ABCA B C so that segment ADA D intersects the interior of ABCA B C, and ∠BAD=∠CAM\angle B A D=\angle C A M. Let ADA D intersect side BCB C at XX. Compute the ratio AX/ADA X / A D.
Plain-text mathematical notation (without MathML)
Let ABC be a triangle with AB=4,BC=8, and CA=5. Let M be the midpoint of BC, and let D be the point on the circumcircle of ABC so that segment AD intersects the interior of ABC, and ∠BAD=∠CAM. Let AD intersect side BC at X. Compute the ratio AX/AD.
Original LaTeX notation
Let $A B C$ be a triangle with $A B=4, B C=8$, and $C A=5$. Let $M$ be the midpoint of $B C$, and let $D$ be the point on the circumcircle of $A B C$ so that segment $A D$ intersects the interior of $A B C$, and $\angle B A D=\angle C A M$. Let $A D$ intersect side $B C$ at $X$. Compute the ratio $A X / A D$.

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task_id
403fcad5-eb9b-5f57-9b84-3e7ce4361bb4
task_key
test--403fcad5-eb9b-5f57-9b84-3e7ce4361bb4
task_revision_id
1
config / split
/ test

Official source

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