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An angle invariant to a certain movable circle

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October 28, 2019
geometrycircumcircleinvariantLocus

Problem Statement

Let R R be the circumradius of a triangle ABC. ABC. The points B,C, B,C, lie on a circle of radius ρ \rho that intersects AB,AC AB,AC at E,D, E,D, respectively. ρ′ \rho' is the circumradius of ADE. ADE. Show that there exists a triangle with sides R,ρ,ρ′, R,\rho ,\rho' , and having an angle whose value doesn't depend on ρ. \rho .
Laurențiu Panaitopol
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