Sides of a triangle are in the ratio 3:4:5. If R denotes circumradius and r denotes inradius then find R/r?

Question

Let ABC be the triangle with AB = 1, AC = 3, and ∠BAC = π/2. If a circle of radius r > 0 touches the sides AB, AC and also touches internally the circumcircle of the triangle ABC, then the value of r is ___.

Answer 1

In radius for a 3,4,5 Pythagorean triangle is 1=r.
R = Circumradius = 3*4*5/(4*r*(3+4+5)/2)
R/r = 3*5/(6) = 2.5.