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A triangle has side lengths of 10, 24, and 26. Let a be the area of the circumcircle. Let b be the area of the incircle. Compute a-b.

 

 

Thanks so much!!!

Noori

 

(Please show steps.) :)
 

 Jun 2, 2020
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Right scalene triangle.

Use Heron's Formula to calculate the area of the triangle and the Law of Cosines to calculate the angles and the radii of the Circumcircle and the Incircle.
Sides: a = 10 b = 24 c = 26

Area: T = 120
Perimeter: p = 60
Semiperimeter: s = 30

 

Angle ∠ A = α = 22.62° = 22°37'11″ = 0.395 rad
Angle ∠ B = β = 67.38° = 67°22'49″ = 1.176 rad
Angle ∠ C = γ = 90° = 1.571 rad

 

Height: ha = 24
Height: hb = 10
Height: hc = 9.231

 

Median: ma = 24.515
Median: mb = 15.62
Median: mc = 13

 

Inradius: r = 4
Circumradius: R = 13
a = Area of Circumcircle =13^2 x Pi
b = Area of Incircle =4^2 x Pi
a  -  b = 153Pi

 Jun 2, 2020

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