[tex] \frac{b}{2}* h_{b}* h_{a}+ \frac{c}{2}* h_{c}* h_{b}+ \frac{a}{2}* h_{c}* h_{a}- \frac{b}{2} * h_{b}* h_{c}- \frac{c}{2}* h_{c}* h_{a}- \\ - \frac{a}{2}* h_{b}* h_{a}= \frac{b}{2}* h_{b}( h_{a}- h_{c})+ \frac{c}{2}* h_{c}( h_{b}- h_{a})+ \frac{a}{2} h_{a }( h_{c}- h_{b})= \\ =A( h_{a}- h_{c}+ h_{b}- h_{a}+ h_{c}- h_{b})=A*0=0 [/tex]
A-aria triunghiului
[tex]A= \frac{a}{2} h_{a}= \frac{b}{2} h_{b}= \frac{c}{2} h_{c} [/tex]
