The diagram shows a triangle (in blue) with side lengths 3-4-5, that has both a circumscribed circle (in green) and a circle inscribed (in red) inside of it. Find the ratio of areas between the larger circle versus the smaller circle.
Right scalene Pythagorean triangle
Use Heron's formula and the Law of Cosines to find the angles and the areas. Or, use Pythagoras's Theorem to do the same thing.
Sides: a = 3 b = 4 c = 5
Area: T = 6
Perimeter: p = 12
Semiperimeter: s = 6
Angle ∠ A = α = 36.87° = 36°52'12″ = 0.644 rad
Angle ∠ B = β = 53.13° = 53°7'48″ = 0.927 rad
Angle ∠ C = γ = 90° = 1.571 rad
Height: ha = 4
Height: hb = 3
Height: hc = 2.4
Median: ma = 4.272
Median: mb = 3.606
Median: mc = 2.5
Inradius: r = 1
Circumradius: R = 2.5
Area of the Incircle =1^2pi
Area Circumcircle =2.5^2pi
Ratio of the areas =1:6.25
