Difference between revisions of "1972 AHSME Problems/Problem 26"

Latest revision as of 15:47, 23 June 2021

Problem

$[asy] real t=pi/8;real u=7*pi/12;real v=13*pi/12; real ct=cos(t);real st=sin(t);real cu=cos(u);real su=sin(u); draw(unitcircle); draw((ct,st)--(-ct,st)--(cos(v),sin(v))); draw((cu,su)--(cu,st)); label("A",(-ct,st),W);label("B",(ct,st),E); label("M",(cu,su),N);label("P",(cu,st),S); label("C",(cos(v),sin(v)),W); //Credit to Zimbalono for the diagram [/asy]$ In the circle above, $M$ is the midpoint of arc $CAB$ and segment $MP$ is perpendicular to chord $AB$ at $P$ . If the measure of chord $AC$ is $x$ and that of segment $AP$ is $(x+1)$ , then segment $PB$ has measure equal to