This website contains problems from math contests. Problems and corresponding tags were obtained from the Art of Problem Solving website.

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Found problems: 2

2014 Contests, 1
The diagram below shows a circle with center $F$. The angles are related with $\angle BFC = 2\angle AFB$, $\angle CFD = 3\angle AFB$, $\angle DFE = 4\angle AFB$, and $\angle EFA = 5\angle AFB$. Find the degree measure of $\angle BFC$. [asy] size(4cm); pen dps = fontsize(10); defaultpen(dps); dotfactor=4; draw(unitcircle); pair A,B,C,D,E,F; A=dir(90); B=dir(66); C=dir(18); D=dir(282); E=dir(210); F=origin; dot("$F$",F,NW); dot("$A$",A,dir(90)); dot("$B$",B,dir(66)); dot("$C$",C,dir(18)); dot("$D$",D,dir(306)); dot("$E$",E,dir(210)); draw(F--E^^F--D^^F--C^^F--B^^F--A); [/asy]
48 degree geometry

2014 Purple Comet Problems, 1
The diagram below shows a circle with center $F$. The angles are related with $\angle BFC = 2\angle AFB$, $\angle CFD = 3\angle AFB$, $\angle DFE = 4\angle AFB$, and $\angle EFA = 5\angle AFB$. Find the degree measure of $\angle BFC$. [asy] size(4cm); pen dps = fontsize(10); defaultpen(dps); dotfactor=4; draw(unitcircle); pair A,B,C,D,E,F; A=dir(90); B=dir(66); C=dir(18); D=dir(282); E=dir(210); F=origin; dot("$F$",F,NW); dot("$A$",A,dir(90)); dot("$B$",B,dir(66)); dot("$C$",C,dir(18)); dot("$D$",D,dir(306)); dot("$E$",E,dir(210)); draw(F--E^^F--D^^F--C^^F--B^^F--A); [/asy]
48 degree geometry