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PUMaC 2014 · 几何（B 组） · 第 4 题

PUMaC 2014 — Geometry (Division B) — Problem 4

专题
Discrete Math / 离散数学
难度
L3
来源
PUMaC

题目详情

  1. [ 4 ] Let O be the circumcenter of triangle ABC with circumradius 15. Let G be the centroid o of ABC and let M be the midpoint of BC . If BC = 18 and ∠ M OA = 150 , find the area of OM G .
解析
  1. [ 4 ] Let O be the circumcenter of triangle ABC with circumradius 15. Let G be the centroid o of ABC and let M be the midpoint of BC . If BC = 18 and \ M OA = 150 , find the area of OM G . Solution: Since O is the circumcenter, we have that OM is perpendicular to BC and so OM B forms an equilateral triangle. Since OB = 15 , BM = 9 ) OM + 12. Then we have that AO = 1 1