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MathNet 2015-part-03 — 191 problems (EN–VI) Question 152

Math Olympiad Vault · MathNet 2015-part-03 — 191 problems (EN–VI)

Question 152

Around the triangle $A B C$ the circle is circumscribed, and at the vertex $C$ tangent $t$ to this circle is drawn. The line $p$ which is parallel to this tangent intersects the lines $B C$ and $A C$ at the points $D$ and $E$, respectively. Prove that the points $A, B, D, E$ belong to the same circle.