PUMaC 2019 · 几何（B 组） · 第 1 题
PUMaC 2019 — Geometry (Division B) — Problem 1
题目详情
- Suppose we have a convex quadrilateral ABCD such that ∠ B = 110 and the circumcircle of 4 ABC has a center at D . Find the measure, in degrees, of ∠ D . Note: The circumcircle of a ∆ ABC is the unique circle containing A, B and C .
解析
- Suppose we have a convex quadrilateral ABCD such that ∠ B = 110 and the circumcircle of 4 ABC has a center at D . Find the measure, in degrees, of ∠ D . Note: The circumcircle of a ∆ ABC is the unique circle containing A, B and C . Proposed by Zachary Stier. Answer: 140 Solution: Draw any point E on the circle, connect it to A and C ; then ABCE is cyclic, so ◦ ∠ E = 70 and since the angles at D and E subtend the same arc, ∠ D = 2 · ∠ E .