用面积法来计算BT的长度

[prq]=2/3[apr]=2/3 * 5/32 *s = 10/96 * s
[tqc]=[aqr] (定理二)
=[apr]+[pqr]
=5/32 * s + 10/96 * s
=25/96 * s

[tqa]=5/3[tqc]=5/3 * 25/96 * s = 125/288 * s
[aqb]=5/8[abc]=5/16 * s
[qbt]=[tqa]-[aqb]=125/288 * s - 5/16 * s
=35/288 * s
AB:QT=[aqb]:[qbt]=(6/16 * s): (35/288 * s) = 18:7
QT=7/18a