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MathNet 2016-part-06 — 184 problems (EN–VI) Question 55

Math Olympiad Vault · MathNet 2016-part-06 — 184 problems (EN–VI)

Question 55

Let $ABC$ be a triangle right-angled at $C$, not isosceles, with legs $b \gt a$.

1. Find the side of the square $AXYZ$ that circumscribes the triangle $ABC$ (the vertices $B$ and $C$ must lie on different sides of the square).

2. Explain step by step how to construct the square $AXYZ$ with ruler and compass.