Y by
*Note: Whenever I have an equation, AoPS gives the error "New users are not allowed to post images in the Community." To circumvent this I've removed all dollar signs from the equations. Sorry for making this unreadable! If anyone has a better solution, please notify me!
Let ABC be a triangle with |AB|\neq|BC| and the circle \omega, passing through the points A and C, intersect sides AB and BC again at points D and E respectively. The tangents to \omega at the points A and E intersect at X. Prove that AC, DE and BX are concurrent.
I stumbled into this result whilst playing around with the nine-point circle. I wasn't able to find this on the internet. If anybody finds it, please reply and give me advice on how to search for such geometry problems! I don't know how to prove this. I can't figure out how to use the tangency.
Let ABC be a triangle with |AB|\neq|BC| and the circle \omega, passing through the points A and C, intersect sides AB and BC again at points D and E respectively. The tangents to \omega at the points A and E intersect at X. Prove that AC, DE and BX are concurrent.
I stumbled into this result whilst playing around with the nine-point circle. I wasn't able to find this on the internet. If anybody finds it, please reply and give me advice on how to search for such geometry problems! I don't know how to prove this. I can't figure out how to use the tangency.
This post has been edited 1 time. Last edited by Gimbrint, Saturday at 10:26 PM
Reason: Added a correction
Reason: Added a correction