HMMT 二月 2011 · TEAM2 赛 · 第 10 题
HMMT February 2011 — TEAM2 Round — Problem 10
题目详情
- [ 15 ] Let the circumcircle of triangle AOM intersect ω again at D . Prove that points A , D , and X are collinear.
解析
- [ 15 ] Let the circumcircle of triangle AOM intersect ω again at D . Prove that points A , D , and X are collinear. Solution: By the similarity 4 OAM ∼ OXA , we have that ∠ OAX = ∠ OM A . Since AOM D is a cyclic quadrilateral, we have that ∠ OM A = ∠ ODA . Since OA = OD , we have that ∠ ODA = ∠ OAD . Combining these equations tells us that ∠ OAX = ∠ OAD , so A , D , and X are collinear, as desired.