Problem

1972 AHSME Problem 26

[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

\textbf{(A) }3x+2\qquad \textbf{(B) }3x+1\qquad \textbf{(C) }2x+3\qquad \textbf{(D) }2x+2\qquad \textbf{(E) }2x+1

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.


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Category: AHSME
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