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Omni-MATH / ABC is a triangle with points E,F on sides AC,AB, respectively. Suppose that BE,CF intersect at X. It is given that AF/FB=(AE/EC)² and that X is the midpoint of BE. Find the ratio …

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problem

ABCA B C is a triangle with points E,FE, F on sides AC,ABA C, A B, respectively. Suppose that BE,CFB E, C F intersect at XX. It is given that AF/FB=(AE/EC)2A F / F B=(A E / E C)^{2} and that XX is the midpoint of BEB E. Find the ratio CX/XFC X / X F.
Plain-text mathematical notation (without MathML)
ABC is a triangle with points E,F on sides AC,AB, respectively. Suppose that BE,CF intersect at X. It is given that AF/FB=(AE/EC)² and that X is the midpoint of BE. Find the ratio CX/XF.
Original LaTeX notation
$A B C$ is a triangle with points $E, F$ on sides $A C, A B$, respectively. Suppose that $B E, C F$ intersect at $X$. It is given that $A F / F B=(A E / E C)^{2}$ and that $X$ is the midpoint of $B E$. Find the ratio $C X / X F$.

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Source and history

task_id
a280eb25-3d40-57e7-9138-0545c449f869
task_key
test--a280eb25-3d40-57e7-9138-0545c449f869
task_revision_id
1
config / split
/ test

Official source

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