##postscript('../WriteUp/Graphics/1984/AIME_prob_6_plot.eps', onefile=FALSE, horizontal=FALSE)

x1 = 14 + seq(-3, +3, length.out=100)
y1_up = 92 + sqrt(9 - (x1-14)^2)
y1_dn = 92 - sqrt(9 - (x1-14)^2)

x2 = 17 + seq(-3, +3, length.out=100)
y2_up = 76 + sqrt(9 - (x2-17)^2)
y2_dn = 76 - sqrt(9 - (x2-17)^2)

x3 = 19 + seq(-3, +3, length.out=100)
y3_up = 84 + sqrt(9 - (x3-19)^2)
y3_dn = 84 - sqrt(9 - (x3-19)^2)

plot(x1, y1_up, asp=1, type='l', col='blue', xlab='x', ylab='y', xlim=c(14-3, 19+3), ylim=c(76-3, 92+3) )
lines(x1, y1_dn, type='l', col='blue')
lines(14, 92, type='p', pch=19, col='blue', cex=1.5)
text(14, 93, '(14, 92)')

lines(x3, y3_up, type='l', col='blue')
lines(x3, y3_dn, type='l', col='blue')
lines(19, 84, type='p', pch=19, col='blue', cex=1.5)
text(19, 85, '(19, 84)')

lines(x2, y2_up, type='l', col='black')
lines(x2, y2_dn, type='l', col='black')
lines(17, 76, type='p', pch=19, col='black', cex=1.5)
text(17, 77, '(17, 76)')

m = -30; abline(-17*m+76, m, col='red') ## plot some lines that might divide the area

grid()
##dev.off()

print( 0.5 * ( c(14, 92) + c(19, 84) ))

print((88 - 76)/(16.5 - 17))