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UKMT Pink Kangaroo, 2015

Geometry Difficulty 2.0 Junior Find the answer United Kingdom

In the triangle $FGH$ , we can draw a line parallel to its base $FG$ , through point $X$ or $Y$ . The areas of the shaded regions are the same. The ratio $HX:XF = 4:1$ . What is the ratio $HY:YF$ ?

(A) $1:1$ (B) $2:1$ (C) $3:1$ (D) $3:2$ (E) $4:3$

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