Thread: Prove that line DF is parallel to BC...

Let ABC be a triangle. Let K be a circle that contains B and C, intersects side AB at a point D between A and B, and intersects side AC at a point E betwen A and C. Let L be a circle that contains D and E and is tangent to line AB. Also assume that L intersects AE at a point F between A and E. Prove that line DF is parallel to line BC.

I've tried everything, any help please?

Hey TimsBobby2.

For these kinds of problems, drawing a diagram is a good place to start since visual cues are often seen and they bring more information than just a purely algebraic formulation would.

Have you drawn a diagram for this problem?

I agree 100% with the previous posting. With the availability of good free/cheap dynamic geometry programs, there's really no excuse not to draw a figure. When you said "K contains B and C", I thought you meant B and C were interior to K or on K. A dynamic geometry program rapidly convinces you that B and C must be on K.

Here's a drawing of your problem together with a solution: