Difference between revisions of "1981 AHSME Problems/Problem 27"
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Revision as of 11:11, 1 December 2022
Problem
In the adjoining figure triangle is inscribed in a circle. Point lies on with , and point lies on with . Side and side each have length equal to the length of chord , and . Chord intersects sides and at and , respectively. The ratio of the area of to the area of is
[asy] defaultpen(linewidth(.8pt)); pair C = origin; pair A = 2.5*dir(75); pair B = A + 2.5*dir(-75); path circ =circumcircle(A,B,C); pair D = waypoint(circ,(7/12)); pair G = waypoint(circ,(1/6)); pair E = intersectionpoint(D--G,A--C); pair F = intersectionpoint(A--B,D--G); label("",A,N); label("",B,SE); label("",C,SW); label("",D,SW); label("",G,NE); label("",E,NW); label("",F,W); label("",A,12S+E,fontsize(6pt)); draw(A--B--C--cycle); draw(circ); draw(Arc(A,0.25,-75,-105)); draw(D--G); [/asy]