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UKMT Maclaurin Olympiad, 2026

Geometry Difficulty 3.0 AMC 10/12 Prove it United Kingdom

A square $ABCD$ has each side of length 1. $X$ lies on $AB$ and $Y$ lies on $AD$ with $AX = x$ , $AY = y$ and $x < y$ . Triangle $AXY$ is removed to leave a pentagon $BCDYX$ . The perimeter of $BCDYX$ is $\frac{29}{30}$ of the perimeter of $ABCD$ . The area of $BCDYX$ is also $\frac{29}{30}$ of the area of $ABCD$ . Find the length of $AX$ .

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