document.write( "Question 1198770: 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? \n" ); document.write( "

Algebra.Com's Answer #832414 by ikleyn(52786) $\"\"$ $\"About$

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\n" ); document.write( "In the figure, P and Q are the centers of two tangent circles and the line PQ intersects the circles
\n" ); document.write( "at Point A and B. The larger circle touches the side CD of the rectangle ABCD at point T.
\n" ); document.write( "If the area of ABCD is 15, what is the area of the triangle PQT?
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document.write( "It is clearly seen from the plot (even by an unarmed eye) that PQ is half of AB,\r\n" );
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document.write( "or, in other words, AB is twice as long as PQ.   (*)\r\n" );
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document.write( "In addition, the height QT of triangle PQT has the same length as the side BC\r\n" );
document.write( "of the rectangle ABCD.\r\n" );
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document.write( "From it, it is clear that the area of the triangle PQT is 1/4 of the area \r\n" );
document.write( "of rectangle ABCD.\r\n" );
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document.write( "ANSWER.  The area of triangle PQT is    square units.\r\n" );
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\n" ); document.write( "\n" ); document.write( "*) It is written in support to my statement (*) above.\r
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\n" ); document.write( "\n" ); document.write( " PQ = r + R; AB = r + r + R + R = 2*(r+R), or AB = 2*PQ.\r
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