Rhombus and inscribed circle

It is given a rhombus with side a = 6 cm and the inscribed circle r = 2 cm radius. Calculate the length of its two diagonals.

Final Answer:

u =  11.2101 cm
v =  4.2819 cm

Step-by-step explanation:

a=6 cm r=2 cm  a = a1​+a2​ r2 = a1​a2​ a1​(a−a1​)= r2  x(6−x)=22  −x2+6x−4=0 x2−6x+4=0  a=1;b=−6;c=4 D=b2−4ac=62−4⋅1⋅4=20 D>0  x1,2​=2a−b±D​​=26±20​​=26±25​​ x1,2​=3±2.236068 x1​=5.236067977 x2​=0.763932023  a1​=x1​=5.2361≐5.2361 a2​=x2​=0.7639≐0.7639  (u/2)2 = a12​ + r2 u=2⋅ a12​+r2​=2⋅ 5.23612+22​=11.2101 cm

Our quadratic equation calculator calculates it.

(v/2)2 = a22​ + r2 v=2⋅ a22​+r2​=2⋅ 0.76392+22​≐4.2819 cm  r2​=a1​⋅ a2​​=5.2361⋅ 0.7639​=2 r2​=r

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