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International Mathematical Olympiad 1959 — Contest Problems Question 6

IMO · International Mathematical Olympiad 1959 — Contest Problems

Question 6

(CZS) Let $\alpha$ and $\beta$ be two planes intersecting at a line $p$. In $\alpha$ a point $A$ is given and in $\beta$ a point $C$ is given, neither of which lies on $p$. Construct $B$ in $\alpha$ and $D$ in $\beta$ such that $ABCD$ is an equilateral trapezoid, $AB\parallel CD$, in which a circle can be inscribed.