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PUMaC 2011 · 几何（B 组） · 第 1 题

PUMaC 2011 — Geometry (Division B) — Problem 1

专题
Discrete Math / 离散数学
难度
L3
来源
PUMaC

题目详情

  1. [ 3 ] Let triangle ABC have ∠ A = 70 , ∠ B = 60 , and ∠ C = 50 . Extend altitude BH past H to point D so that BD = BC . Find ∠ BDA in degrees.
解析
  1. Because ∠ A = 70 , we know that ∠ ABH = 20 , so ∠ HBC = 40 . Constructing DC , we have ◦ that triangle BDC is isosceles, so ∠ BDC = ∠ BCD = 70 . Noticing that ∠ BAC = ∠ BDC = ◦ ◦ 70 , we have that quadrilateral ABCD is cyclic. It follows that ∠ BDA = ∠ BCA = 50 . Figure 1: Problem 1 diagram. Figure 2: Problem 2 diagram.