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The formula calculates the fourth side (Side D) of a cyclic quadrilateral when the perimeter and the other three sides are known. A cyclic quadrilateral is a four-sided polygon where all vertices lie on a single circle.
The calculator uses the formula:
Where:
Explanation: This formula is derived from the basic perimeter formula of a quadrilateral, where the perimeter equals the sum of all four sides.
Details: Calculating the missing side of a cyclic quadrilateral is essential in geometry problems, architectural design, and various engineering applications where precise measurements are required.
Tips: Enter the perimeter and the three known sides in meters. All values must be positive numbers. The calculator will compute the fourth side automatically.
Q1: What is a cyclic quadrilateral?
A: A cyclic quadrilateral is a four-sided polygon where all vertices lie on a single circle, also known as an inscribed quadrilateral.
Q2: Can this formula be used for any quadrilateral?
A: This specific formula works for any quadrilateral, not just cyclic ones, as it's based on the basic perimeter calculation.
Q3: What units should I use for the inputs?
A: The calculator uses meters, but you can use any consistent unit of length as long as all measurements are in the same unit.
Q4: What if the calculated side D is negative?
A: A negative result indicates that the sum of the three given sides exceeds the perimeter, which is mathematically impossible for a valid quadrilateral.
Q5: Are there other properties specific to cyclic quadrilaterals?
A: Yes, cyclic quadrilaterals have special properties like opposite angles summing to 180 degrees (supplementary angles) and Ptolemy's theorem relationships.