Državno natjecanje 2010 SŠ2 4
Dodao/la:
arhiva1. travnja 2012. Upisana kružnica dodiruje stranice
![\overline{AB}](/media/m/a/1/a/a1a42310b1a849922197735f632d57ec.png)
i
![\overline{AC}](/media/m/d/9/5/d95354f0f833a5fda9c16a01a878c14f.png)
trokuta
![ABC](/media/m/a/c/7/ac75dca5ddb22ad70f492e2e0a153f95.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/6/b/9/6b9d0901c0aea1638a561ba96a7d740e.png)
. Dokaži da je
![BP \perp CP](/media/m/a/e/5/ae52bf8327e71e2bc74b0662f1057490.png)
.
%V0
Upisana kružnica dodiruje stranice $\overline{AB}$ i $\overline{AC}$ trokuta $ABC$ u točkama $M$ i $N$. Neka je $P$ sjecište pravca $MN$ i simetrale kuta $\angle{ABC}$. Dokaži da je $BP \perp CP$.
Izvor: Državno natjecanje iz matematike 2010