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Fie \( ABC \) un triunghi \( A \) - isoscel cu \( A = 40^{\circ} \). Notam:

\( M\in (AB)\ ,\ MA = MC \); \( N\in (MC)\ ,\ AN\perp BC \);

\( P\in (AN)\ ,\ PN = NC \). Sa se arate ca \( PM = PA \) .

\( MC=MA \Rightarrow MCA=40^{\circ}\Rightarrow DCN=30^{\circ} \Rightarrow \)
\( DNC=60^{\circ} \Rightarrow NPC=NCP=30^{\circ} \Rightarrow \)
\( PC=2DC=BC \Rightarrow \Delta PMC=\Delta MBC\Rightarrow \)
\( PMC=80^{\circ}\Rightarrow PMA=20^{\circ}\Rightarrow AP=PM. \)