document.write( "Question 34510: A triangle with sides of 5, 12 and 13 has both an inscribed and a circumscribed circle. What is the distance between the centers of those circles. \n" ); document.write( "

Algebra.Com's Answer #20810 by venugopalramana(3286) $\"\"$ $\"About$

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WE FIND THAT 5^2+12^2=25+144=169=13^2...SO IT IS RIGHT ANGLED TRIANGLE..IF
\n" ); document.write( "LET OA=5,OB=12,AB=13...THEN ANGLE AOB =90....LET O BE ORIGIN.SO A IS (5,0) AND B IS (0,12).SO CIRCUM CENTRE S IS THE MID POINT OF AB THE HYPOTENUSE.
\n" ); document.write( "HENCE S IS {5/2,12/2)=(5/2,6)
\n" ); document.write( "INCENTRE I IS GIVEN BY
\n" ); document.write( "X COORDINATE....(5*0+12*5+13*0)/(5+12+13)=60/30=2
\n" ); document.write( "Y COORDINATE....(5*12+12*0+13*0)/(5+12+13)=60/30=2
\n" ); document.write( "HENCE S IS (2,2)
\n" ); document.write( "SI =SQRT.{(5/2-2)^2+(6-2)^2}=SQRT(1/4+16)=SQRT(16.25) \n" ); document.write( "

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