U šiljastokutnom trokutu
![ABC](/media/m/a/c/7/ac75dca5ddb22ad70f492e2e0a153f95.png)
označimo s
![D](/media/m/7/0/0/7006c4b57335ab717f8f20960577a9ef.png)
diralište pripisane kružnice i stranice
![\overline{BC}](/media/m/8/8/1/8818caad7d36e134c54122cbf46f1cd9.png)
, a
![E](/media/m/8/b/0/8b01e755d2253cb9a52f9e451d89ec11.png)
diralište upisane kružnice i stranice
![\overline{BC}](/media/m/8/8/1/8818caad7d36e134c54122cbf46f1cd9.png)
. Neka je
![I_1](/media/m/4/1/6/416fe38d243ecd6d66747e4d88b6518d.png)
središte upisane kružnice trokuta
![ABD](/media/m/a/5/4/a548bc577543629d304ecba1a042f910.png)
, a
![I_2](/media/m/c/b/0/cb0739259063636b82f7b6b3e9dd3de0.png)
središte upisane kružnice trokuta
![ADC](/media/m/b/5/b/b5ba4f2dbf8650a6779ccd5923a7f007.png)
. Dokažite da je
![EDI_1I_2](/media/m/7/4/e/74e840de352860e3769c83db040e81fb.png)
tetivan.
%V0
U šiljastokutnom trokutu $ABC$ označimo s $D$ diralište pripisane kružnice i stranice $\overline{BC}$, a $E$ diralište upisane kružnice i stranice $\overline{BC}$. Neka je $I_1$ središte upisane kružnice trokuta $ABD$, a $I_2$ središte upisane kružnice trokuta $ADC$. Dokažite da je $EDI_1I_2$ tetivan.