HMMT 十一月 2010 · 冲刺赛 · 第 16 题
HMMT November 2010 — Guts Round — Problem 16
题目详情
- [ 9 ] Triangle ABC is given in the plane. Let AD be the angle bisector of ∠ BAC ; let BE be the altitude from B to AD , and let F be the midpoint of AB . Given that AB = 28 , BC = 33 , CA = 37, what is the length of EF ? Page 1 of 3
解析
- [ 9 ] Triangle ABC is given in the plane. Let AD be the angle bisector of ∠ BAC ; let BE be the altitude from B to AD , and let F be the midpoint of AB . Given that AB = 28 , BC = 33 , CA = 37, what is the length of EF ? Answer: 14 4 ABE is a right triangle, and F is the midpoint of the hypotenuse (and therefore the circumcenter), so EF = BF = AF = 14.