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Omni-MATH / Let ABC be an isosceles triangle with AB=AC. Let D and E be the midpoints of segments AB and AC, respectively. Suppose that there exists a point F on ray (DE)→ outside of ABC such …

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problem

Let ABCA B C be an isosceles triangle with AB=ACA B=A C. Let DD and EE be the midpoints of segments ABA B and ACA C, respectively. Suppose that there exists a point FF on ray DE→\overrightarrow{D E} outside of ABCA B C such that triangle BFAB F A is similar to triangle ABCA B C. Compute ABBC\frac{A B}{B C}.
Plain-text mathematical notation (without MathML)
Let ABC be an isosceles triangle with AB=AC. Let D and E be the midpoints of segments AB and AC, respectively. Suppose that there exists a point F on ray (DE)→ outside of ABC such that triangle BFA is similar to triangle ABC. Compute (AB)/(BC).
Original LaTeX notation
Let $A B C$ be an isosceles triangle with $A B=A C$. Let $D$ and $E$ be the midpoints of segments $A B$ and $A C$, respectively. Suppose that there exists a point $F$ on ray $\overrightarrow{D E}$ outside of $A B C$ such that triangle $B F A$ is similar to triangle $A B C$. Compute $\frac{A B}{B C}$.

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Source and history

task_id
277d47d1-b206-5a81-b372-9693db6374ea
task_key
test--277d47d1-b206-5a81-b372-9693db6374ea
task_revision_id
1
config / split
/ test

Official source

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