PUMaC 2021 · 个人决赛（A 组） · 第 2 题

PUMaC 2021 — Individual Finals (Division A) — Problem 2

Let ABCD be a cyclic quadrilateral with circumcircle Γ, and let E be the midpoint of the diag- onal BD . Let I , I , I , I be the centers of the circles inscribed into triangles △ ABE, △ ADE, 1 2 3 4 △ BCE, △ CDE , in that order. Prove that the circles AI I and CI I intersect Γ at diamet- 1 2 3 4 rically opposite points. Remark: For a circle C and points X, Y ∈ C , we say that X and Y are diametrically opposite if XY is a diameter of C .

解析

暂无解答链接。

No solutions link available.