22
Part of 2015 AMC 10
Problems(2)
No two Coins Adjacent
Source: 2015 AMC 12A #17/10A #22
2/4/2015
Eight people are sitting around a circular table, each holding a fair coin. All eight people flip their coins and those who flip heads stand while those who flip tails remain seated. What is the probability that no two adjacent people will stand?
probabilityAMCAMC 12countingdistinguishabilityAMC10
Pentagon Ratios
Source: 2015 AMC 10B #22
2/26/2015
In the figure shown below, is a regular pentagon and . What is ?
[asy]
import cse5;pathpen=black;pointpen=black;
size(2inch);
pair A=dir(90), B=dir(18), C=dir(306), D=dir(234), E=dir(162);
D(MP("A",A,A)--MP("B",B,B)--MP("C",C,C)--MP("D",D,D)--MP("E",E,E)--cycle,linewidth(1.5));
D(A--C--E--B--D--cycle);
pair F=IP(A--D,B--E), G=IP(B--E,C--A), H=IP(C--A,B--D), I=IP(D--B,E--C), J=IP(C--E,D--A);
D(MP("F",F,dir(126))--MP("I",I,dir(270))--MP("G",G,dir(54))--MP("J",J,dir(198))--MP("H",H,dir(342))--cycle);
[/asy]
ratioAsymptotetrigonometryUSAMTSgeometryparallelogramangle bisector