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Omni-MATH / Let A,B,C,D,E,F be 6 points on a circle in that order. Let X be the intersection of AD and BE, Y is the intersection of AD and CF, and Z is the intersection of CF and BE. X lies on…

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problem

Let A,B,C,D,E,FA, B, C, D, E, F be 6 points on a circle in that order. Let XX be the intersection of ADAD and BEBE, YY is the intersection of ADAD and CFCF, and ZZ is the intersection of CFCF and BEBE. XX lies on segments BZBZ and AYAY and YY lies on segment CZCZ. Given that AX=3,BX=2,CY=4,DY=10,EZ=16AX=3, BX=2, CY=4, DY=10, EZ=16, and FZ=12FZ=12, find the perimeter of triangle XYZXYZ.
Plain-text mathematical notation (without MathML)
Let A,B,C,D,E,F be 6 points on a circle in that order. Let X be the intersection of AD and BE, Y is the intersection of AD and CF, and Z is the intersection of CF and BE. X lies on segments BZ and AY and Y lies on segment CZ. Given that AX=3,BX=2,CY=4,DY=10,EZ=16, and FZ=12, find the perimeter of triangle XYZ.
Original LaTeX notation
Let $A, B, C, D, E, F$ be 6 points on a circle in that order. Let $X$ be the intersection of $AD$ and $BE$, $Y$ is the intersection of $AD$ and $CF$, and $Z$ is the intersection of $CF$ and $BE$. $X$ lies on segments $BZ$ and $AY$ and $Y$ lies on segment $CZ$. Given that $AX=3, BX=2, CY=4, DY=10, EZ=16$, and $FZ=12$, find the perimeter of triangle $XYZ$.

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Source and history

task_id
aff399c0-b09c-5d75-bd35-4bce60e505b4
task_key
test--aff399c0-b09c-5d75-bd35-4bce60e505b4
task_revision_id
1
config / split
/ test

Official source

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