document.write( "Question 1028878: the tangency point of a circle,inscribed in a right angled triangle ,divides its hypotenuse by the segment 5cm and 12cm.find the triangles legs \n" ); document.write( "

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\n" ); document.write( "the tangency point of a circle,inscribed in a right angled triangle ,divides its hypotenuse by the segment 5cm and 12cm.find the triangles legs
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\n" ); document.write( "\n" ); document.write( "Answer. The legs are 8 cm and 15 cm.\r
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document.write( "Let \"r\" be the radius of the inscribed circle.\r\n" );
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document.write( "Then one leg is (5+r) cm long, and the other leg is (12+r) cm.\r\n" );
document.write( "(Make a sketch and use the fact that the tangent segments from the point outside the circle are congruent).\r\n" );
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document.write( "Then you have this quadratic equation to find \"r\" (Pythagorean, of course).\r\n" );
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document.write( " = .\r\n" );
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document.write( "Simplify and solve it. It is arithmetics.\r\n" );
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document.write( "The solution is r = 3.\r\n" );
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document.write( "Then the legs are 5+3 = 8 cm  and  12+3 = 15 cm.\r\n" );
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