Tangent circles

Geometry Level 3

A circle of radius $3~cm$ is inscribed in a square as shown. A small circle is inscribed between the two sides of the square and the big circle. Which of the following is the most approximate area of the shaded region in $cm^2$ ? Use $\pi=3.14$

1.1 3.1 0.1 2.1

1 solution

A Former Brilliant Member
Sep 23, 2017

let $DE=DF=CF=r$ , then, $CD=r\sqrt{2}$

It follows that, $AC=3\sqrt{2}$ .

$AC=3+DE+CD$ $\implies$ $3\sqrt{2}=3+r+r\sqrt{2}$ $\implies$ $r \approx 0.51$

$A_{shaded}=\dfrac{6^2-(3.14)(3^2)}{4}-(3.14)(0.51^2) \approx$ $\color{#D61F06}\boxed{1.1~cm^2}$

Tangent circles

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