Unutar šiljastokutnog trokuta
![ABC](/media/m/a/c/7/ac75dca5ddb22ad70f492e2e0a153f95.png)
nalazi se točka
![P](/media/m/9/6/8/968d210d037e7e95372de185e8fb8759.png)
takva da je
![\angle{APB}=\angle{CBA}+\angle{ACB}, \qquad \angle{BPC}=\angle{ACB}+\angle{BAC}.](/media/m/d/0/a/d0a95f660871c89d6518686f107cb4aa.png)
Dokaži da vrijedi
%V0
Unutar šiljastokutnog trokuta $ABC$ nalazi se točka $P$ takva da je $$\angle{APB}=\angle{CBA}+\angle{ACB}, \qquad \angle{BPC}=\angle{ACB}+\angle{BAC}.$$
Dokaži da vrijedi $$\frac{|AC|\cdot |BP|}{|BC|}=\frac{|BC|\cdot |AP|}{|AB|}.$$