stoyan_rysinov
New member
- Joined
- Mar 22, 2020
- Messages
- 1
A triangle[MATH] ABC[/MATH] is given and two points[MATH] P_1[/MATH] and [MATH]P_2 [/MATH]inside it.
We know that:
[MATH]AP_1\cap BC=A_1[/MATH], [MATH]BP_1\cap AC=B_1[/MATH],[MATH] CP_1\cap AB=C_1[/MATH], [MATH]AP_2\cap BC=A_2[/MATH], [MATH]BP_2\cap AC=B_2[/MATH], [MATH]CP_2\cap AB=C_2[/MATH]. We also know that: [MATH]A_1B_1\cap B_2C_2=N[/MATH], [MATH]A_1C_1\cap B_2C_2=P[/MATH] and[MATH] A_1C_1\cap A_2B_2=M[/MATH].
Show that [MATH]AM,BN[/MATH] and [MATH]CP[/MATH] are concurrent.
I think we can use Ceva's Theorem for the concurrence of cevians in a triangle. Can you help me?
We know that:
[MATH]AP_1\cap BC=A_1[/MATH], [MATH]BP_1\cap AC=B_1[/MATH],[MATH] CP_1\cap AB=C_1[/MATH], [MATH]AP_2\cap BC=A_2[/MATH], [MATH]BP_2\cap AC=B_2[/MATH], [MATH]CP_2\cap AB=C_2[/MATH]. We also know that: [MATH]A_1B_1\cap B_2C_2=N[/MATH], [MATH]A_1C_1\cap B_2C_2=P[/MATH] and[MATH] A_1C_1\cap A_2B_2=M[/MATH].
Show that [MATH]AM,BN[/MATH] and [MATH]CP[/MATH] are concurrent.
I think we can use Ceva's Theorem for the concurrence of cevians in a triangle. Can you help me?