Answer:
<h2>
a-b = 156π</h2>
Step-by-step explanation:
<u>For the inscribed circle</u>
Formula for calculating the radius of an inscribed circle in a triangle r = Area of the triangle/0.5 of its perimeter
Given a triangle of side 10, 24 and 26.
Area of the triangle = 1/2 * base * height
Area of the triangle = 1/2*10*24
Area of the triangle = 120
Perimeter of the triangle = 10+24+26 = 60
radius of the inscribed circle = 120/0.5(60)
r = 120/30
r = 4
Area of the incircle b = πr² = π(4)² = 16π
<u>For the circumcircle</u>
Formula for calculating the radius of a circumcircle outside a triangle
R = abc/4√s(s-a)(s-b)(s-c)
s = a+b+c/2
a, b and c are the length of the 3 sides
s = 10+24+26/2
s = 60/2 = 30
R = 10(24)(26)/4√30(20)(6)(4)
R = 6240/4*120
R = 13
radius of the circumcircle = 13
Area of the circumcircle a = πR² = π(13)² = 169π
a - b = 169π - 16π
<h3>
a-b = 156π</h3>
