Given a semicircle with radius r, we have to find the largest square that can be inscribed in the semicircle, with base lying on the diameter.
Input: r = 5 Output: 20 Input: r = 8 Output: 51.2
Approach: Let r be the radius of the semicircle & a be the side length of the square.
From the figure we can see that, centre of the circle is also the midpoint of the base of the square.So in the right angled triangle AOB, from Pythagorus Theorem:
a^2 + (a/2)^2 = r^2
5*(a^2/4) = r^2
a^2 = 4*(r^2/5) i.e. area of the square
Below is the implementation of the above approach:
- Largest ellipse that can be inscribed within a rectangle which in turn is inscribed within a semicircle
- Largest rectangle that can be inscribed in a semicircle
- Largest trapezoid that can be inscribed in a semicircle
- Largest triangle that can be inscribed in a semicircle
- Area of largest Circle that can be inscribed in a SemiCircle
- Biggest Reuleaux Triangle inscirbed within a square inscribed in a semicircle
- Largest square that can be inscribed within a hexagon which is inscribed within an equilateral triangle
- Area of largest semicircle that can be drawn inside a square
- Largest Square that can be inscribed within a hexagon
- Largest hexagon that can be inscribed within a square
- Area of a circle inscribed in a rectangle which is inscribed in a semicircle
- Area of the Largest square that can be inscribed in an ellipse
- Biggest Reuleaux Triangle inscribed within a square which is inscribed within an ellipse
- Biggest Reuleaux Triangle inscribed within a square which is inscribed within a hexagon
- Area of a square inscribed in a circle which is inscribed in an equilateral triangle
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