哇塞，貌如巩俐算玑珠。

第一眼，看到或许在ABDF中算拖罗密，有些边没有一眼看出来。转念一想，这里面有三个直角，从解析几何的角度，一下子关系就看出来了。

From Heron's formula, it is easy to see AD=12, BD=5, and DC=9.

Let D be the origin (0,0), BD sit on x-axis to have A(0,12), B(-5,0) and C(9,0).

Let F coordinates be (x,y).

Since DE is perpendicular to AC, so y/x = -(9-0)/(0-12)=3/4, which is 4y-3x=0 --------(1)

In the same time AF is perpendicular to BF, (y-0)/(x+5)=-(x-0)/(y-12), which is 4x+3y=16 -------(2)

Square both sides of (1) and (2), we have:

16y^2 + 9x^2 -24xy = 0 ------(3)
16x^2 + 9y^2 +24xy = 16^2 -------(4)

Add (3) to (4), 25x^2 + 25y^2 = 16^2 i.e. sqrt(x^2+y^2)=16/5=DF.

所有跟帖： 

• Actually it is pretty easy to use ptolemy theorem too since it i -calligraphy- ♂ (0 bytes) () 12/05/2014 postreply 05:13:49