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.

Question 34511: 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) (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)
RELATED QUESTIONS
A triangle with sides of 5, 12 and 13 has both an inscribed and a circumscribed circle.... (answered by venugopalramana)

A hexagon of side length 4cm has both an inscribed and a circumscribed circle. What is... (answered by ikleyn)

What is the difference in area between the inscribed circle and the circumscribed circle (answered by MathLover1,Edwin McCravy,ikleyn)

A circle of radius 1, and corresponding inscribed and circumscribed polygons with the... (answered by solver91311)

For this exercise, consider a circle of radius 1, and corresponding inscribed and... (answered by KMST)

If a circle is inscribed in a triangle with sides 12, 12, and 8, what is the radius of... (answered by Mathtut)

Three sides of a triangle measure 12 in, 15 in and 18 in. Find the area of the triangle,... (answered by rothauserc)

A circle is inscribed in a given square and another circle is circumscribed about the... (answered by ankor@dixie-net.com)

A triangle with sides of length 36 cm, 77 cm, and 85 cm are inscribed in a circle. Inside (answered by ikleyn)