HMMT 二月 2006 · 几何 · 第 2 题
HMMT February 2006 — Geometry — Problem 2
题目详情
英文原题
- Suppose ABC is a scalene right triangle, and P is the point on hypotenuse AC such
°
that ∠ ABP = 45 . Given that AP = 1 and CP = 2, compute the area of ABC .
解析
英文解析
- Suppose ABC is a scalene right triangle, and P is the point on hypotenuse AC such
°
that ∠ ABP = 45 . Given that AP = 1 and CP = 2, compute the area of ABC .
Answer:9
Solution: Notice that BP bisects the right angle at B . Thus, we write AB = 2 x ,5
2 21
BC = x . By the Pythagorean theorem, 5 x = 9, from which the area ( x )(2 x ) = x =
.92 5