Side A of Cyclic Quadrilateral given both Diagonals Calculator

Formula Used:

\[ Side A = \frac{(Diagonal 1 \times Diagonal 2) - (Side B \times Side D)}{Side C} \]

Diagonal 1 of Cyclic Quadrilateral:

Diagonal 2 of Cyclic Quadrilateral:

Side B of Cyclic Quadrilateral:

Side D of Cyclic Quadrilateral:

Side C of Cyclic Quadrilateral:

Side A of Cyclic Quadrilateral:

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1. What is the Side A of Cyclic Quadrilateral given both Diagonals Formula?

The formula calculates Side A of a cyclic quadrilateral using both diagonals and the other three sides. It's derived from Ptolemy's theorem and the properties of cyclic quadrilaterals.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ Side A = \frac{(Diagonal 1 \times Diagonal 2) - (Side B \times Side D)}{Side C} \]

Where:

\( Diagonal 1 \) — First diagonal of the cyclic quadrilateral (m)
\( Diagonal 2 \) — Second diagonal of the cyclic quadrilateral (m)
\( Side B \) — One of the sides of the cyclic quadrilateral (m)
\( Side D \) — Another side of the cyclic quadrilateral (m)
\( Side C \) — The remaining side of the cyclic quadrilateral (m)

Explanation: This formula is derived from the properties of cyclic quadrilaterals where opposite angles sum to 180 degrees and Ptolemy's theorem applies.

3. Importance of Cyclic Quadrilateral Calculations

Details: Calculating sides and diagonals of cyclic quadrilaterals is crucial in geometry, engineering design, and architectural planning where circular patterns and cyclic properties are involved.

4. Using the Calculator

Tips: Enter all measurements in meters. Ensure all values are positive and non-zero. The calculator provides precise results for geometric calculations involving cyclic quadrilaterals.

5. Frequently Asked Questions (FAQ)

Q1: What is a cyclic quadrilateral?
A: A cyclic quadrilateral is a four-sided polygon where all vertices lie on a single circle.

Q2: Why is this formula important?
A: It allows calculation of an unknown side when both diagonals and the other three sides are known, which is useful in various geometric applications.

Q3: What are the limitations of this formula?
A: The formula assumes the quadrilateral is cyclic and all measurements are accurate. It may not work for non-cyclic quadrilaterals.

Q4: Can this formula be used for any quadrilateral?
A: No, this formula specifically applies to cyclic quadrilaterals where all vertices lie on a circle.

Q5: How accurate are the results?
A: The results are mathematically precise based on the input values, assuming the quadrilateral is truly cyclic.