Kamp '13 - Angle Chasing 15.
Dodao/la:
arhiva3. studenoga 2013. Upisana kružnica dodiruje stranice
![AB](/media/m/5/2/9/5298bd9e7bc202ac21c423e51da3758e.png)
i
![AC](/media/m/6/4/7/647ef3a5d68f07d59d84afe03a9dc655.png)
trokuta
![\triangle ABC](/media/m/1/f/3/1f3c3c0f3e134a169655f9511ba6ea82.png)
u točkama
![M](/media/m/f/7/f/f7f312cf6ba459a332de8db3b8f906c4.png)
i
![N](/media/m/f/1/9/f19700f291b1f2255b011c11d686a4cd.png)
. Neka je
![P](/media/m/9/6/8/968d210d037e7e95372de185e8fb8759.png)
sjecište pravca
![MN](/media/m/2/6/7/267a73297a5de9e529d41774ee6ff45a.png)
i simetrale kuta
![\angle ABC](/media/m/c/9/2/c92dca0f4ca20d0ca087b59e09a26fa8.png)
. Dokažite da je
![BP \perp CP](/media/m/a/e/5/ae52bf8327e71e2bc74b0662f1057490.png)
.
%V0
Upisana kružnica dodiruje stranice $AB$ i $AC$ trokuta $\triangle ABC$ u točkama $M$ i $N$. Neka je $P$ sjecište pravca $MN$ i simetrale kuta $\angle ABC$. Dokažite da je $BP \perp CP$.
Izvor: Kamp 2013. - Angle Chasing, L. V.