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IMAS 2024–2025 — Upper Primary — Round 2 Question 7

IMAS · IMAS 2024–2025 — Upper Primary — Round 2

Question 7

In triangle ABC, $\angle ACB=30^\circ$ and $\angle BAC=90^\circ$, where D is a point on BC. Points X and Y are on AD such that the areas of triangles AXB, AXC, XBY, XCY and YBC are all equal, as shown in the diagram below.

Question illustration

If $AB=25$ cm, what is the length, in cm, of XY?