Right triangle inradius and circumradius
In a right triangle if inradius = r, hypotenuse = c and legs are a,b then: r = (a + b - c)/2 Proof: From the center of the incircle, the perpendiculars are dropped on the 2 legs (a,b). It creates a square and splits the base in 2 parts r, a-r and similarly the other leg is split into r,b-r. Since 2 tangents from one point are equal => c = a - r + b - r => r = (a + b - c)/2 Circumradius of a right triangle = c/2 where c is hypotenuse. Proof: Easy by co-ordinate geometry. A = (0,0) B = (a,0) C = (0,b) Midpoint of BC = a/2,b/2 OA = OB = OC = sqrt(a^2/4 + b^2/4) => O is the circumcenter and OA = Hypotenuse/2 = Circumradius.