Mathematics - Properties of Triangle Question with Solution | TestHub

The area is 6 $c{m}^2$ and semiperimeter is 6 cm, so r=1 cm; R=5/2 cm. Euler's identity $O{I}^2$=R(R-2r)=(5/2)(1/2)=5/4, giving OI=$\sqrt{5}$/2 cm. Alternatively, with the right angle at (0,0), circumcenter (1.5,2) and incenter (1,1), their separation is $\sqrt{(.5{)}^2+1^2}$=$\sqrt{5}$/2.