HMMT 二月 2000 · 几何 · 第 7 题
HMMT February 2000 — Geometry — Problem 7
题目详情
英文原题
- Let AB C be a triangle ins rib ed in the ellipse + = 1. If its en troid is the origin
4 9
(0,0), nd its area.
15 p
解析
英文解析
- Let's "resize" the o ordinates to be x = x; y = . This k eeps the origin at (0,0), butturns our ellipse in to a ir le of radius 2. Th us no w, the triangle is equilateral, and we A3
G 1 hh
F2
C Bb
E D2
an see it no w has area 3 3. On e we expand ba k, we an see we are just m ultiplyingpp
9 3
the area b y and so the answ er is .3
ab sin A22