Now, the maximum length of a and b will always be strictly less than the diameter of the circle so all possible values of a and b will lie in the closed interval. Thus, all the combinations of a and b can be checked to form all possible rectangles, and if the diagonal of any such rectangle is less than or equal to the length of the diagonal of the largest rectangle formed (i.e 2 * R, where R is the Radius of the circle as explained above) The diameter BD is the maximum diagonal the rectangle can have to be able to be cut from the Circular Sheet. ∴ AD = AB by CPCT(i.e Corresponding Parts on Congruent Triangles) Its easy to see, that ABCD is the largest rectangle that can be formed in the given circle with radius R and centre O, having dimensions a X bĭrop a perpendicular AO such that, ∠AOD = ∠AOB = 90°Ĭonsider the following diagram for further analysis, Recommended: Please solve it on “ PRACTICE ” first, before moving on to the solution Check whether triangle is valid or not if sides are given.How to check if a given point lies inside or outside a polygon?.Therefore, the surface area is the sum of the areas of the two circles. How to check if two given line segments intersect? forms a rectangle with height h and width equal to the circumference of the can.Closest Pair of Points using Divide and Conquer algorithm.Count Inversions in an array | Set 1 (Using Merge Sort).One of the properties of a rectangle is that the diagonals bisect in the 'center' of the. Actually - every rectangle can be inscribed in a (unique circle) so the key point is that the radius of the circle is R (I think). Count inversions in an array | Set 3 (Using BIT) Thus, the rectangle's area is constrained between 0 and that of the square whose diagonal length is 2R. ![]() The usual approach to solving this type of problem is calculus’ optimization. Count smaller elements on right side and greater elements on left side using Binary Index Tree Answer (1 of 9): The largest rectangle that can be inscribed in a circle is a square.Count smaller elements on right side using Set in C++ STL.Number of swaps to sort when only adjacent swapping allowed.Minimum number of swaps required to sort an array of first N number.Minimum number of swaps required to sort an array | Set 2.Minimum number of swaps required to sort an array.Minimum swaps to make two arrays consisting unique elements identical.Largest permutation after at most k swaps.Largest lexicographic array with at-most K consecutive swaps.Lexicographically smallest array after at-most K consecutive swaps.Paper Cut into Minimum Number of Squares.Minimum squares to evenly cut a rectangle.Number of squares of maximum area in a rectangle.Number of rectangles in a circle of radius R.The biggest possible circle that can be inscribed in a rectangle.ISRO CS Syllabus for Scientist/Engineer Exam.ISRO CS Original Papers and Official Keys.GATE CS Original Papers and Official Keys.Notices of the American Mathematical Society. I haven't found any good page on evaluating if a number of given circles is able to fill a rectangle. with a minimum radius of N homogeneous circles covering a square. Many covering problems are concerned e.g. It's difficult to find some good information on this. ![]() "Circle Packing: A Mathematical Tale" (PDF). I understand, your problem then becomes a covering problem, not a packing problem. The Penguin Dictionary of Curious and Interesting Geometry. ![]()
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