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AIMO 2021 Secondary 2 — Preliminary (Open Trial 1) Question 8

AIMO · AIMO 2021 Secondary 2 — Preliminary (Open Trial 1)

Question 8

In right triangle $EXO$, $\angle E=90^\circ$. Point $F$ lies on $XO$ and $EF\perp XO$. If $EO=2$ and $XE=3$, find the area of triangle $EFO$.

Original printed choices: A: $\frac{54}{160}$; B: $\frac{54}{25}$; C: $\frac{25}{16}$; D: $\frac{21}{16}$.

Editorial response format: give the exact answer; the original choices are retained for reference.

Question illustration