The Great Division

Level pending

A B D C ABDC is a square. E; F; G; H; I; J; K \text{E; F; G; H; I; J; K} are the midpoints of DB; DC; EF; BE; CF; GH; GI \text{DB; DC; EF; BE; CF; GH; GI} . JK \text{JK} intersect DB \text{DB} at L L , intersect DC \text{DC} at M M . Calculate E F ⋅ H I L M \frac{\sqrt{EF \cdot HI}}{LM} .

6 5 \frac{6}{5} 72 25 \sqrt{\frac{72}{25}} 1 12 25 \sqrt{\frac{12}{25}} 24 25 \sqrt{\frac{24}{25}}

Thành Đạt Lê by Thành Đạt Lê , 17, Singapore

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