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Side C of Cyclic Quadrilateral is one of the four sides of a cyclic quadrilateral, which is a quadrilateral whose vertices all lie on a single circle. In a cyclic quadrilateral, the sum of opposite angles is always 180 degrees.
The calculator uses the formula:
Where:
Explanation: This formula calculates the unknown side C by subtracting the sum of the other three known sides from the total perimeter of the cyclic quadrilateral.
Details: Calculating sides of cyclic quadrilaterals is important in geometry, architecture, and engineering applications where circular patterns and cyclic properties are utilized. Understanding these relationships helps in solving complex geometric problems and designing structures with specific geometric properties.
Tips: Enter the perimeter and the three known sides (A, B, and D) in meters. All values must be positive numbers. The calculator will compute Side C by subtracting the sum of the three known sides from the total perimeter.
Q1: What is a cyclic quadrilateral?
A: A cyclic quadrilateral is a four-sided polygon whose vertices all lie on a single circle. This property gives it special geometric characteristics, such as the sum of opposite angles being 180 degrees.
Q2: Can this formula be used for any quadrilateral?
A: This specific formula works for any quadrilateral where the perimeter and three sides are known, regardless of whether it's cyclic or not. However, the cyclic property is mentioned as it's the context of this calculator.
Q3: What units should I use for the inputs?
A: The calculator uses meters as the default unit, 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 C is negative?
A: A negative result indicates that the sum of the three known sides exceeds the total perimeter, which is geometrically impossible. Please double-check your input values.
Q5: Are there other ways to calculate sides of cyclic quadrilaterals?
A: Yes, using trigonometric relationships and the cyclic quadrilateral theorems (such as Ptolemy's theorem), but this perimeter-based method is the simplest when the perimeter and other sides are known.