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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.

 

 Jun 5, 2020
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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

 Jun 5, 2020

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