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The computation shows the radius of the circle that is inscribed in the isosceles triangle will be 3.33cm.
From the information given, the isosceles triangle the length of a base is 10 cm and the length of a leg is 13 cm.
Let A = area of the triangle
Let S = semi perimeter of the triangle.
The radius will be: = A/S
where,
[tex]S = \dfrac{(a + b + c)}{2} = \dfrac{(13 + 13 + 10)}{2} = 18[/tex]
The radius will be:
[tex]=\dfrac{(\sqrt{18} - \sqrt{13})(\sqrt{18} - \sqrt{13})(\sqrt{18} - \sqrt{10})} { 18}[/tex]
= 3.33cm
In conclusion, the radius is 3.33cm.
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