Perechi de drepte care se intalnesc pe circumcerc.

[Virgil Nicula]

Fie triunghiul \( ABC \) inscris in cercul \( w \) . Notam \( \left\|\begin{array}{ccc}
D\in (BC) & , & \widehat {DAB}\equiv\widehat{DAC}\\\\\\\\\\\
S\in AD\cap w & , & S\not\equiv A\end{array}\right\| \) si mijloacele \( M \) , \( N \) ,

\( P \) ale segmentelor \( (AB) \) , \( (AD) \) , \( (AC) \) respectiv. Sa se arate ca \( (SM\cap CN)\cup (SP\cap BN)\subset w \) .

[Marius Mainea]

\( \triangle{ASM}\sim\triangle{ACN} \) si de aici \( \angle{ASM}=\angle{ACN} \)