a) Fie MP∩AC={R} si
CP∩AM={Q}
Fie BD=a=DM (inaltimea e si mediana)⇒BN=AB/2=BC/2=2a/2=a
darMB=BD=a
⇒ΔBMNtr.issoscelde baza MN
m∡MBN=180°-60°=120°⇒m∡BMN=(180°-120°)/2=30°
dar m∡BCA=60°⇒m∡MRC=180°-30°-60°=90°⇔MR⊥AC
MR⊥AC (pctul a)
AD⊥BC (ipoteza)⇒P, ortocentru ΔAMC⇒CP⊥AM