RT and circles

Solve the right triangle if the radius of the inscribed circle is r=9 and the radius of the circumscribed circle is R=26.

Final Answer:

a =  46.27
b =  23.73
c =  52

Step-by-step explanation:

r=9 R=26  R = 2c​ c=2⋅ R=2⋅ 26=52  r = 2a+b−c​ 2r+c = a+b a+b = 70 a + b = 70  a2 + b2 = c2  a2+(70−a)2=c2  a2+(70−a)2=522 2a2−140a+2196=0 2 ...  prime number 140=22⋅5⋅7 2196=22⋅32⋅61 GCD(2,140,2196)=2  a2−70a+1098=0  p=1;q=−70;r=1098 D=q2−4pr=702−4⋅1⋅1098=508 D>0  a1,2​=2p−q±D​​=270±508​​=270±2127​​ a1,2​=35±11.269428 a1​=46.26942767 a2​=23.73057233  a=a1​=46.2694=46.27

Our quadratic equation calculator calculates it.

b=70−a=70−46.2694=23.73

Try calculation via our triangle calculator.


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