Proving a property of the Morley Triangle
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I'm trying to prove the following property of Morley's Theorem.
Let ABC be a triangle and apply Morley's Theorem to form a Morley triangle with vertices M, L, and K. Connecting the vertices of ABC to vertices of triangle MLK form lines AM, BL, and CK. Prove that these lines are concurrent.
I've tried using Ceva's Theorem to determine where AM meets BC but I'm getting lost. Any ideas for an alternate proof or some help using Ceva's to prove concurrence?
Thank you.
euclidean-geometry triangle
edited Nov 17 at 21:19
José Carlos Santos
144k20112213
asked Nov 17 at 21:18
c14emmons
24
add a comment |
up vote
0
down vote
favorite
I'm trying to prove the following property of Morley's Theorem.
Let ABC be a triangle and apply Morley's Theorem to form a Morley triangle with vertices M, L, and K. Connecting the vertices of ABC to vertices of triangle MLK form lines AM, BL, and CK. Prove that these lines are concurrent.
I've tried using Ceva's Theorem to determine where AM meets BC but I'm getting lost. Any ideas for an alternate proof or some help using Ceva's to prove concurrence?
Thank you.
euclidean-geometry triangle
edited Nov 17 at 21:19
José Carlos Santos
144k20112213
asked Nov 17 at 21:18
c14emmons
24
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
I'm trying to prove the following property of Morley's Theorem.
Let ABC be a triangle and apply Morley's Theorem to form a Morley triangle with vertices M, L, and K. Connecting the vertices of ABC to vertices of triangle MLK form lines AM, BL, and CK. Prove that these lines are concurrent.
I've tried using Ceva's Theorem to determine where AM meets BC but I'm getting lost. Any ideas for an alternate proof or some help using Ceva's to prove concurrence?
Thank you.
euclidean-geometry triangle
edited Nov 17 at 21:19
José Carlos Santos
144k20112213
asked Nov 17 at 21:18
c14emmons
24
I'm trying to prove the following property of Morley's Theorem.
Let ABC be a triangle and apply Morley's Theorem to form a Morley triangle with vertices M, L, and K. Connecting the vertices of ABC to vertices of triangle MLK form lines AM, BL, and CK. Prove that these lines are concurrent.
I've tried using Ceva's Theorem to determine where AM meets BC but I'm getting lost. Any ideas for an alternate proof or some help using Ceva's to prove concurrence?
Thank you.
euclidean-geometry triangle
euclidean-geometry triangle
edited Nov 17 at 21:19
José Carlos Santos
144k20112213
asked Nov 17 at 21:18
c14emmons
24
edited Nov 17 at 21:19
José Carlos Santos
144k20112213
asked Nov 17 at 21:18
c14emmons
24
edited Nov 17 at 21:19
José Carlos Santos
144k20112213
edited Nov 17 at 21:19
José Carlos Santos
144k20112213
edited Nov 17 at 21:19
José Carlos Santos
144k20112213
144k20112213
asked Nov 17 at 21:18
c14emmons
24
asked Nov 17 at 21:18
c14emmons
24
asked Nov 17 at 21:18
c14emmons
24
24
add a comment |
add a comment |
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