Given here is a circle of a given radius. Inside it, three tangent circles of equal radius are inscribed. The task is to find the radii of these tangent circles.
Input: R = 4 Output: 1.858 Input: R = 11 Output:: 5.1095
- Let the radii of the tangent circles be r, and the radius of the circumscribing circle
is R.x is the smaller distance from the circumference of the tangent circle and the center of the circumscribing circle.
- From the diagram, it is very clear,
2r + x = R
- now in triangle OBC,
cos 30 = r/(r+x)
rcos30 + xcos30 = r
x = r(1-cos30)/cos30
- also, x = R-2r
R-2r = r(1-cos30)/cos30
R-2r = 0.133r/0.867
R-2r = 0.153r
R = 2.153r
so, r = 0.4645R
The radii of the tangent circles is 1.858
Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.
- Radius of the inscribed circle within three tangent circles
- Find the radii of the circles which are lined in a row, and distance between the centers of first and last circle is given
- Largest square that can be inscribed within a hexagon which is inscribed within an equilateral triangle
- Largest right circular cylinder that can be inscribed within a cone which is in turn inscribed within a cube
- Biggest Reuleaux Triangle inscribed within a square which is inscribed within an ellipse
- Largest right circular cone that can be inscribed within a sphere which is inscribed within a cube
- Biggest Reuleaux Triangle inscribed within a square which is inscribed within a hexagon
- Largest sphere that can be inscribed within a cube which is in turn inscribed within a right circular cone
- Largest ellipse that can be inscribed within a rectangle which in turn is inscribed within a semicircle
- Radius of the biggest possible circle inscribed in rhombus which in turn is inscribed in a rectangle
- Biggest Reuleaux Triangle within a Square which is inscribed within a Circle
- Distance between centers of two intersecting circles if the radii and common chord length is given
- Biggest Reuleaux Triangle within a Square which is inscribed within a Right angle Triangle
- Area of a square inscribed in a circle which is inscribed in an equilateral triangle
- Area of a circle inscribed in a rectangle which is inscribed in a semicircle
- Area of a square inscribed in a circle which is inscribed in a hexagon
- Biggest Reuleaux Triangle inscribed within a Square inscribed in an equilateral triangle
- Area of Equilateral triangle inscribed in a Circle of radius R
- Length of the transverse common tangent between the two non intersecting circles
- Length of the direct common tangent between two externally touching circles
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.