SOLUTION: 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.

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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.
Answer by venugopalramana(3286) About Me  (Show Source):
You can put this solution on YOUR website!
WE FIND THAT 5^2+12^2=25+144=169=13^2...SO IT IS RIGHT ANGLED TRIANGLE..IF
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.
HENCE S IS {5/2,12/2)=(5/2,6)
INCENTRE I IS GIVEN BY
X COORDINATE....(5*0+12*5+13*0)/(5+12+13)=60/30=2
Y COORDINATE....(5*12+12*0+13*0)/(5+12+13)=60/30=2
HENCE S IS (2,2)
SI =SQRT.{(5/2-2)^2+(6-2)^2}=SQRT(1/4+16)=SQRT(16.25)