document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1198770>Question 1198770</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In the figure, P and Q are the centers of two tangent circles and the line PQ intersects the circles at Point A and B. The larger circle touches the side CD of the rectangle ABCD at point T. If the area of ABCD is 15, what is the area of the triangle PQT? </SPAN>\n" );
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document.write( "I'll reference the diagram @lotusjayden has posted.\r<BR>\n" );
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document.write( "AB*BC = 15 since the rectangle ABCD has area 15 square units.\r<BR>\n" );
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document.write( "AB = AP+PR+RQ+QB<BR>\n" );
document.write( "where R is the point of tangency between circles P and Q.\r<BR>\n" );
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document.write( "AP = PR as they are radii of circle P<BR>\n" );
document.write( "RQ = QB as they are radii of circle Q\r<BR>\n" );
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document.write( "So,<BR>\n" );
document.write( "AB = AP+PR+RQ+QB<BR>\n" );
document.write( "AB = PR+PR+RQ+RQ<BR>\n" );
document.write( "AB = 2(PR+RQ)<BR>\n" );
document.write( "AB = 2*PQ<BR>\n" );
document.write( "PQ = 0.5*AB\r<BR>\n" );
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document.write( "Then,<BR>\n" );
document.write( "area of triangle PQT = 0.5*base*height<BR>\n" );
document.write( "area of triangle PQT = 0.5*PQ*QT<BR>\n" );
document.write( "area of triangle PQT = 0.5*(0.5*AB)*BC<BR>\n" );
document.write( "area of triangle PQT = 0.25*AB*BC<BR>\n" );
document.write( "area of triangle PQT = 0.25*(area of rectangle ABCD)<BR>\n" );
document.write( "area of triangle PQT = 0.25*(15)<BR>\n" );
document.write( "area of triangle PQT = 3.75 square units<BR>\n" );
document.write( "This converts to the improper fraction 15/4.<BR>\n" );
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