三角形APM相似于三角形CPR,可知CR=5/6DC
除非指明,下面出现的全部是向量,除了s, t, 和常数。
令BA = a,BC = b, BS = t * b (0 < t < 1)
BR = b + 5/6 * a
QC = 3/8 * AC = 3/8 * (a - b)
BQ = b + QC = 3/8 * a + 5/8 * b
Q在线段RS上,所以存在 s, 0 < s < 1, 满足
BQ = s * BR + (1 - s) * BS
= s * (b + 5/6 * a) + (1 - s) * t * b
= 5/6 * s* a + (s + (1 - s) * t) * b
= 3/8 * a + 5/8 * b
于是
5/6 * s = 3/8
s + (1 - s) * t = 5/8
解得
s = 9/20
t = 7/22