Dan je trokut
![ABC](/media/m/a/c/7/ac75dca5ddb22ad70f492e2e0a153f95.png)
. Simetrala kuta
![\angle CAB](/media/m/4/c/8/4c8433a2baf2fc63fcfcfd6b2715c08b.png)
siječe stranicu
![\overline{BC}](/media/m/8/8/1/8818caad7d36e134c54122cbf46f1cd9.png)
u točki
![D](/media/m/7/0/0/7006c4b57335ab717f8f20960577a9ef.png)
, a simetrala kuta
![\angle ABC](/media/m/c/9/2/c92dca0f4ca20d0ca087b59e09a26fa8.png)
siječe stranicu
![\overline{AC}](/media/m/d/9/5/d95354f0f833a5fda9c16a01a878c14f.png)
u točki
![E](/media/m/8/b/0/8b01e755d2253cb9a52f9e451d89ec11.png)
. Ako je
![\angle ACB \ge 60^\circ](/media/m/0/c/6/0c674ec0d4ee048bea2a95d614fcf347.png)
, dokaži da je
![|AE|+|BD|\le |AB|](/media/m/c/1/7/c172d11d50ccce53187994d88a2ac9a0.png)
.
%V0
Dan je trokut $ABC$. Simetrala kuta $\angle CAB$ siječe stranicu $\overline{BC}$ u točki $D$, a simetrala kuta $\angle ABC$ siječe stranicu $\overline{AC}$ u točki $E$. Ako je $\angle ACB \ge 60^\circ$, dokaži da je $|AE|+|BD|\le |AB|$.