Side D Of Cyclic Quadrilateral Given Both Diagonals Calculator

Formula Used:

\[ Sd = \frac{(d1 \times d2) - (Sa \times Sc)}{Sb} \]

Diagonal 1 of Cyclic Quadrilateral:

Diagonal 2 of Cyclic Quadrilateral:

Side A of Cyclic Quadrilateral:

Side C of Cyclic Quadrilateral:

Side B of Cyclic Quadrilateral:

Side D of Cyclic Quadrilateral:

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1. What is the Side D of Cyclic Quadrilateral Formula?

The formula calculates the length of side D in a cyclic quadrilateral using the lengths of both diagonals and the other three sides. This formula is derived from Ptolemy's theorem and the properties of cyclic quadrilaterals.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ Sd = \frac{(d1 \times d2) - (Sa \times Sc)}{Sb} \]

Where:

\( Sd \) — Side D of Cyclic Quadrilateral (m)
\( d1 \) — Diagonal 1 of Cyclic Quadrilateral (m)
\( d2 \) — Diagonal 2 of Cyclic Quadrilateral (m)
\( Sa \) — Side A of Cyclic Quadrilateral (m)
\( Sc \) — Side C of Cyclic Quadrilateral (m)
\( Sb \) — Side B of Cyclic Quadrilateral (m)

Explanation: This formula calculates the length of the fourth side of a cyclic quadrilateral when both diagonals and the other three sides are known.

3. Importance of Cyclic Quadrilateral Calculations

Details: Calculating side lengths in cyclic quadrilaterals is important in geometry, engineering, and architectural design where circular patterns and cyclic properties are involved.

4. Using the Calculator

Tips: Enter all values in meters. All inputs must be positive numbers greater than zero. The calculator will compute the length of side D based on the provided values.

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: This formula helps determine unknown side lengths in cyclic quadrilaterals when both diagonals and other sides are known.

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.