Given an ellipse, with major axis length 2a & 2b, the task is to find the area of the largest triangle that can be inscribed in it.
Input: a = 4, b = 2 Output: 10.3923 Input: a = 5, b = 3 Output: 10.8253
Approach: So we know the ellipse is just the scaled shadow of a circle.Let’s find the scaling factor.
x^2/a^2 + y^2/b^2 = 1 is an ellipse. Rewrite this as:
(y*(a/b))^2+x^2 = a^2
This is just a vertically scaled down circle of radius a (think light falls from the top at an angle), and the vertical factor is a/b. The biggest triangle in the ellipse is then a scaled up version of the biggest triangle in the circle. Using a little geometry and taking symmetry into account, we can understand that the biggest such triangle is the equilateral one. It’s sides will be √3a and the area will be (3√3)a^2/4
Translating this to ellipse terms – we scale the horizontal dimension up by a factor a/b, and the area of the biggest triangle in the ellipse is,
A = (3√3)a^2/4b
Below is the implementation of above approach:
- Biggest Reuleaux Triangle inscribed within a square which is inscribed within an ellipse
- Area of a triangle inscribed in a rectangle which is inscribed in an ellipse
- Largest ellipse that can be inscribed within a rectangle which in turn is inscribed within a semicircle
- Largest square that can be inscribed within a hexagon which is inscribed within an equilateral triangle
- Area of the Largest square that can be inscribed in an ellipse
- Area of Largest rectangle that can be inscribed in an Ellipse
- Find the area of largest circle inscribed in ellipse
- Largest triangle that can be inscribed in a semicircle
- Largest hexagon that can be inscribed within an equilateral triangle
- Area of largest triangle that can be inscribed within a rectangle
- Area of the Largest Triangle inscribed in a Hexagon
- Biggest Reuleaux Triangle inscribed within a Square inscribed in an equilateral triangle
- Area of a square inscribed in a circle which is inscribed in an equilateral triangle
- Biggest Reuleaux Triangle inscribed within a square which is inscribed within a hexagon
- Biggest Reuleaux Triangle within a Square which is inscribed within a Right angle Triangle
If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to firstname.lastname@example.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.