Općinsko natjecanje 1995 SŠ2 4
Dodao/la:
arhiva2. travnja 2012. Unutar trokuta
![ABC](/media/m/a/c/7/ac75dca5ddb22ad70f492e2e0a153f95.png)
nalazi se točka
![R](/media/m/4/d/7/4d76ce566584cfe8ff88e5f3e8b8e823.png)
. Paralela sa stranicom
![\overline{AB}](/media/m/a/1/a/a1a42310b1a849922197735f632d57ec.png)
kroz
![R](/media/m/4/d/7/4d76ce566584cfe8ff88e5f3e8b8e823.png)
siječe stranice
![\overline{AC}](/media/m/d/9/5/d95354f0f833a5fda9c16a01a878c14f.png)
i
![\overline{BC}](/media/m/8/8/1/8818caad7d36e134c54122cbf46f1cd9.png)
u točkama
![M](/media/m/f/7/f/f7f312cf6ba459a332de8db3b8f906c4.png)
i
![N](/media/m/f/1/9/f19700f291b1f2255b011c11d686a4cd.png)
, paralela sa stranicom
![\overline{AC}](/media/m/d/9/5/d95354f0f833a5fda9c16a01a878c14f.png)
kroz
![R](/media/m/4/d/7/4d76ce566584cfe8ff88e5f3e8b8e823.png)
siječe
![\overline{BC}](/media/m/8/8/1/8818caad7d36e134c54122cbf46f1cd9.png)
i
![\overline{AB}](/media/m/a/1/a/a1a42310b1a849922197735f632d57ec.png)
u točkama
![E](/media/m/8/b/0/8b01e755d2253cb9a52f9e451d89ec11.png)
i
![F](/media/m/3/e/8/3e8bad5df716d332365fca76f53c1743.png)
, a paralela sa stranicom
![\overline{BC}](/media/m/8/8/1/8818caad7d36e134c54122cbf46f1cd9.png)
kroz
![R](/media/m/4/d/7/4d76ce566584cfe8ff88e5f3e8b8e823.png)
siječe
![\overline{AB}](/media/m/a/1/a/a1a42310b1a849922197735f632d57ec.png)
i
![\overline{AC}](/media/m/d/9/5/d95354f0f833a5fda9c16a01a878c14f.png)
u
![K](/media/m/e/1/e/e1ed1943d69f4d6a840e99c7bd199930.png)
i
![P](/media/m/9/6/8/968d210d037e7e95372de185e8fb8759.png)
. Površine trokuta
![NER](/media/m/8/d/4/8d4dc4a7b97359d80282fed8a6069255.png)
,
![PMR](/media/m/7/2/d/72db88015c4c644ef992c951c94bec74.png)
i
![FKR](/media/m/6/1/d/61ded9f9cfd3f313e4cf72a876178945.png)
iznose redom
![a^{2}, b^{2}, c^{2}](/media/m/5/a/3/5a3488e7a92ff62ab7a970638b962c93.png)
. Odredite površinu trokuta
![ABC](/media/m/a/c/7/ac75dca5ddb22ad70f492e2e0a153f95.png)
.
%V0
Unutar trokuta $ABC$ nalazi se točka $R$. Paralela sa stranicom $\overline{AB}$ kroz $R$ siječe stranice $\overline{AC}$ i $\overline{BC}$ u točkama $M$ i $N$, paralela sa stranicom $\overline{AC}$ kroz $R$ siječe $\overline{BC}$ i $\overline{AB}$ u točkama $E$ i $F$, a paralela sa stranicom $\overline{BC}$ kroz $R$ siječe $\overline{AB}$ i $\overline{AC}$ u $K$ i $P$. Površine trokuta $NER$, $PMR$ i $FKR$ iznose redom $a^{2}, b^{2}, c^{2}$. Odredite površinu trokuta $ABC$.
Izvor: Općinsko natjecanje iz matematike 1995