DP=PC; AB = 2BC → BC = AB/2 = DC/2 = PC. Deci BC=CP → ΔPCB = isoscel → PBC=CPB. Dar DC║AB si PB = secanta → CPB=ABP, dar CPB=CBP → CBP=PBA → PB = bisectoarea ABC.
AD=DP (deoarece AB = DC = 2BC → ΔADP = isoscel → DAP=DPA. DC║AB si AP = secanta → DPA=PAB. Dar DPA=DAP → DAP=PAB → AP = bisectoarea DAB