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Questions  >>  Olympiad-Math  >>  Class 10
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Q)

Area of the largest circle that can be inscribed in a semicircle of radius ‘r’ units is

$\begin{array}{1 1}(A) \; \sqrt 2 r^2 sq.units \\(B)\;r^2 sq.units \\(C)\;\large\frac{r^2}{\sqrt 2} sq.units\\(D)\; \large\frac{r^2}{2} sq.units \end{array}$

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A)
Here Diameter of circle = Radius of semicircle =r
Radius of the circle $= \large\frac{r}{2}$
Area of the circle $= \pi \bigg( \large\frac{r}{2}\bigg)^2 =\frac{\pi r^2}{4}$
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