Kamp '13 - Geometrija 14.
Dodao/la:
arhiva3. studenoga 2013. Neka je točka
![P](/media/m/9/6/8/968d210d037e7e95372de185e8fb8759.png)
unutar
![ABC](/media/m/a/c/7/ac75dca5ddb22ad70f492e2e0a153f95.png)
. Pravci
![AP](/media/m/7/b/0/7b05fe3b464ec24a15fa5701f4d14b61.png)
,
![BP](/media/m/e/e/f/eefb4fe46ab8d85b7067c29b24aa4cfc.png)
,
![CP](/media/m/6/3/0/630424587cadeb75669118dab3df6b98.png)
sijeku opisanu kružnicu
![ABC](/media/m/a/c/7/ac75dca5ddb22ad70f492e2e0a153f95.png)
u redom
![K](/media/m/e/1/e/e1ed1943d69f4d6a840e99c7bd199930.png)
,
![L](/media/m/f/c/1/fc1ae4eb78da7d1352cbf1f8217ab286.png)
,
![M](/media/m/f/7/f/f7f312cf6ba459a332de8db3b8f906c4.png)
. Tangenta na opisanu kružnicu u
![C](/media/m/5/a/b/5ab88f3f735b691e133767fe7ea0483c.png)
siječe
![AB](/media/m/5/2/9/5298bd9e7bc202ac21c423e51da3758e.png)
u
![S](/media/m/c/6/3/c63593c3ec0773fa38c2659e08119a75.png)
. Dokaži da
![SC = SP \Rightarrow MK = ML](/media/m/8/f/0/8f06bae698da0f633c9416076b719898.png)
.
%V0
Neka je točka $P$ unutar $ABC$. Pravci $AP$, $BP$, $CP$ sijeku opisanu kružnicu $ABC$ u redom $K$, $L$, $M$. Tangenta na opisanu kružnicu u $C$ siječe $AB$ u $S$. Dokaži da $SC = SP \Rightarrow MK = ML$.
Izvor: Kamp 2013. - Geometrija, M. M.