Circles 2

Calculate the area bounded by the circumscribed and inscribed circle in triangle with sides 12 cm, 14 cm, 18 cm.

Correct result:

S =  209.4 cm2

Solution:

s=12+14+182=22 cm S1=22(2212)(2214)(2218)=83.9 cm2 ρ=S1s=3.81 cm r=abc4S1=121418483.9=9.01 cm  S=π(r2ρ2)=209.4 cm2s = \dfrac{ 12 + 14+ 18}{2} = 22 \ \text{cm} \ \\ S_1 = \sqrt{ 22 \cdot (22-12)\cdot (22-14)\cdot (22-18)} = 83.9 \ \text{cm}^2 \ \\ \rho = \dfrac{ S_1}{ s} = 3.81 \ \text{cm} \ \\ r = \dfrac{ abc}{ 4 S_1} = \dfrac{ 12\cdot 14\cdot 18}{ 4 \cdot 83.9} = 9.01 \ \text{cm} \ \\ \ \\ S = \pi(r^2 - \rho^2) = 209.4 \ \text{cm}^2



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