Silly geo

by shiningsunnyday, Apr 10, 2017, 2:01 PM

2013 USAMO P1 wrote:
In triangle $ABC$, points $P$, $Q$, $R$ lie on sides $BC$, $CA$, $AB$ respectively. Let $\omega_A$, $\omega_B$, $\omega_C$ denote the circumcircles of triangles $AQR$, $BRP$, $CPQ$, respectively. Given the fact that segment $AP$ intersects $\omega_A$, $\omega_B$, $\omega_C$ again at $X$, $Y$, $Z$, respectively, prove that $YX/XZ=BP/PC$.

Solution

Tidbit
geometry
Angle Chasing
Solved

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9 Comments

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i agree this is quite silly

by wu2481632, Apr 10, 2017, 2:34 PM

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i agree with the above statement

by BobThePotato, Apr 10, 2017, 2:35 PM

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i agree geo is quite silly

by 62861, Apr 10, 2017, 3:37 PM

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i disagree with CantonMathGuy :furious:

by wu2481632, Apr 10, 2017, 3:40 PM

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i agree with CantonMathGuy :wow:

by zephyrcrush78, Apr 10, 2017, 4:36 PM

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How dare you!!11!1!!

by shiningsunnyday, Apr 10, 2017, 6:11 PM

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I learned what a spiral similarity was when reading Yufei Zhao's Lemmas several months ago ...

Also the title is inaccurate only complex bash is silly

by MathAwesome123, Apr 11, 2017, 12:05 AM

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complex bash is the ichiban method

by zephyrcrush78, Apr 11, 2017, 1:00 AM

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you are all silly
only bary bash can be true silly

by agbdmrbirdyface, Apr 11, 2017, 3:45 AM

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

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