Inverting into a Trash Can

by agbdmrbirdyface, Aug 17, 2016, 3:20 AM

According to most nerds (like us on AoPS), we have often been subject to inversion and subsequent stuffing in trash cans.

Perhaps this inversion will not be so bad?
#9 in 110 Problems in Oly Geo, mild paraphrasing wrote:
Let $ ABC $ be a triangle with $ \angle BAC < \angle ACB .$ Let $ D, E $ be points on sides $AC, AB$, respectively, such that the angles $\angle ACB$ and $\angle BED$ are congruent. If $F$ lies in the interior of quadrilateral $BCDE$ such that the circles $(BCF)$ and $(DEF)$ are tangent, and circles $(BEF)$ and $(CDF)$ are tangent, show the points $A, C, E, F$ are concyclic.

Solution:

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5 Comments

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NO MORE INVERSION JOKES PLEASE PLEASE PLEASE

by phi_ftw1618, Aug 17, 2016, 6:38 AM

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Wait oops really busy, will do this later

by shiningsunnyday, Aug 17, 2016, 8:07 AM

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Cute inversion that gets rid of the wacky angle condition! I think we did harder inversion problems that featured more wacky angle conditions... Rip geo 3 days...

by shiningsunnyday, Aug 18, 2016, 2:21 AM

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The wacky angle condition plagued me in drawing the diagram :(

thank the geogebra gods

by agbdmrbirdyface, Aug 18, 2016, 7:21 PM

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"I'll invert your face about ISIS"

by phi_ftw1618, Aug 19, 2016, 1:22 AM

To share with readers my favorite problem I came across today :) (Shout for contrib.)

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