Radius of incircle and circumcircle in a right triangle as well as general case

Radius of incircle and circumcircle in a right triangle as well as general case

[xsilata]

for a triangle with a side ratio of 3:4:5 there is also a chord ratio for an inscribed circle.
Hypotenuse 3:2
Small leg 2:1
Big leg 3:1

[ЗояШаромет]

r=полупериметр минус гипотенуза. ( 5+4+3)/2-5=1.

[harikatragadda]

1)Diameter of a circle makes 90º on the circumference. Hence Circumradius R=5/2
2)Incircle radius of a Right Triangle r = 1/2*(Altitude + Base - Hypotenuse) = 1 (easy to prove this relationship)

[VolkGreg]

Define D, E, F as the intersections of the circle with sides AB, BC, CA respectively.

AC = AF + FC = AD + EC = (AB - r) + (BC - r)
5 = 3 + 4 - 2r
r = 1

[amadeus]

Sence the tangent of a circle meeting at a point are equal in length.
Therefore we can say 5 -( 3- r ) = 4 - r
Solving the equation we get r = 1