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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.

 Jul 18, 2020
 #1
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a - b = 144*pi - 16*pi = 128*pi.

 Jul 18, 2020
 #2
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How did you come up with 144pi? Can you explain it?

Guest Jul 18, 2020
 #3
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This is very easy!smiley

Hints:

1/    This is the right triangle.

2/    Find the area of a triangle using Heron's formula.

3/    r = A/s

4/    R = abc/4rs

Enough from melaugh

 Jul 18, 2020
 #4
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Right scalene triangle.
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

 

Inradius: r = 4
Circumradius: R = 13


Area =Pi x r^2
Area of the Circumcircle =Pi x 13^2
Area of the Incircle           =Pi x 4^2
[a - b] =13^2Pi - 4^2Pi
[a - b] = 153Pi

 Jul 18, 2020

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