Given two circles of radius r and R, both have their centre at the origin. Now, given another circle of radius r1 and centre at (x1, y1). Check, if the third circle(circle of radius r1) lies completely inside the ring formed by two circles of radius r and R.
Input : r = 8 R = 4 r1 = 2 x1 = 6 y1 = 0 Output : yes Input : r = 8 R = 4 r1 = 2 x1 = 5 y1 = 0 Output : no
Important : Concentric circles are those circles which have same centre. The region lying between two concentric circles is called annulus or the circular ring.
There are two concentric circles with their centre at origin(0, 0) and radius as r = 8 and R = 4.
1.) Circle 1 and 2 lies inside the ring.
2.) Circle 3 and 4 are outside the ring.
The complete figure can be visualised as given below :
This problem can be solved using Pythagoras Theorem . Compute the distance between the centre of the circle and origin using Pythagoras theorem, suppose it is denoted by ‘dis’.
After computing the distance just check that the value of (dis – r1)> = r and (dis + r1)< = R. If both these conditions hold then the circle lies completely inside the ring.
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.
- Check if a circle lies inside another circle or not
- Program to calculate the area between two Concentric Circles
- Find if a point lies inside a Circle
- Ratio of the distance between the centers of the circles and the point of intersection of two direct common tangents to the circles
- Ratio of the distance between the centers of the circles and the point of intersection of two transverse common tangents to the circles
- Check if the given point lies inside given N points of a Convex Polygon
- Check whether given circle resides in boundary maintained by two other circles
- Check whether a given point lies inside a triangle or not
- How to check if a given point lies inside or outside a polygon?
- Check whether a given point lies inside a rectangle or not
- Check whether a given point lies on or inside the rectangle | Set 3
- Check whether a point lies inside a sphere or not
- Check if a point lies on or inside a rectangle | Set-2
- Find a point that lies inside exactly K given squares
- Count of integral coordinates that lies inside a Square
- Find if a point lies inside, outside or on the circumcircle of three points A, B, C
- Radii of the three tangent circles of equal radius which are inscribed within a circle of given radius
- Find the radii of the circles which are lined in a row, and distance between the centers of first and last circle is given
- Program to check if N is a Concentric Hexagonal Number
- Radius of the inscribed circle within three tangent circles
Improved By : jit_t