U trokutu
![ABC](/media/m/a/c/7/ac75dca5ddb22ad70f492e2e0a153f95.png)
vrijedi
![\angle{ACB} = 90^{\circ} + \frac{1}{2} \angle{CBA}](/media/m/a/2/1/a213a51c7c5b7bc3c316a6638c3c0137.png)
, a
![M](/media/m/f/7/f/f7f312cf6ba459a332de8db3b8f906c4.png)
je polovište dužine
![\overline{BC}](/media/m/8/8/1/8818caad7d36e134c54122cbf46f1cd9.png)
. Kružnica sa središtem u točki
![A](/media/m/5/a/e/5ae81275ee67d638485e903bdc0e9cde.png)
siječe pravac
![BC](/media/m/5/0/0/5005d4d5eac1b420fbabb76c83fc63ad.png)
u točkama
![M](/media/m/f/7/f/f7f312cf6ba459a332de8db3b8f906c4.png)
i
![D](/media/m/7/0/0/7006c4b57335ab717f8f20960577a9ef.png)
.
Dokaži da je
![\left\vert MD \right\vert = \left\vert AB \right\vert](/media/m/6/3/3/633655432c4a3a9090a41ed266321fd8.png)
.
%V0
U trokutu $ABC$ vrijedi $\angle{ACB} = 90^{\circ} + \frac{1}{2} \angle{CBA}$, a $M$ je polovište dužine $\overline{BC}$. Kružnica sa središtem u točki $A$ siječe pravac $BC$ u točkama $M$ i $D$.
Dokaži da je $\left\vert MD \right\vert = \left\vert AB \right\vert$.