Cetermine the length of AB - [Canadian Repêchage 2011]
Source:
January 15, 2011
trigonometrygeometry proposedgeometry
Problem Statement
In the diagram, the circle has radius and and centre Points and are on the circle. If and determine the length of
[asy]
import graph; size(120); real lsf = 0.5; pen dp = linewidth(0.7) + fontsize(10); defaultpen(dp); pen ds = black; pen qqttff = rgb(0,0.2,1); pen xdxdff = rgb(0.49,0.49,1); pen fftttt = rgb(1,0.2,0.2);
draw(circle((2.34,2.4),2.01),qqttff); draw((2.34,2.4)--(1.09,0.82),fftttt); draw((2.34,2.4)--(4.1,1.41),fftttt); draw((1.09,0.82)--(1.4,4.18),fftttt); draw((4.1,1.41)--(1.4,4.18),fftttt);
dot((2.34,2.4),ds); label("", (2.1,2.66),NE*lsf); dot((1.09,0.82),ds); label("", (0.86,0.46),NE*lsf); dot((4.1,1.41),ds); label("", (4.2,1.08),NE*lsf); dot((1.4,4.18),ds); label("", (1.22,4.48),NE*lsf); clip((-4.34,-10.94)--(-4.34,6.3)--(16.14,6.3)--(16.14,-10.94)--cycle);
[/asy]