Side C Of Cyclic Quadrilateral Given Both Diagonals Calculator

Formula Used:

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

Diagonal 1 of Cyclic Quadrilateral:

Diagonal 2 of Cyclic Quadrilateral:

Side B of Cyclic Quadrilateral:

Side D of Cyclic Quadrilateral:

Side A of Cyclic Quadrilateral:

Side C of Cyclic Quadrilateral:

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

The formula calculates Side C of a cyclic quadrilateral using both diagonals and the other three sides. A cyclic quadrilateral is a four-sided polygon whose vertices all lie on a single circle.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

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

Explanation: This formula is derived from Ptolemy's theorem and the properties of cyclic quadrilaterals, relating the sides and diagonals of the quadrilateral.

3. Importance of Cyclic Quadrilateral Calculations

Details: Understanding cyclic quadrilateral properties is essential in geometry, engineering, and architectural design where circular patterns and cyclic shapes are common.

4. Using the Calculator

Tips: Enter all measurements in meters. Ensure all values are positive numbers greater than zero for accurate calculations.

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, also known as an inscribed quadrilateral.

Q2: What is Ptolemy's theorem?
A: Ptolemy's theorem states that for a cyclic quadrilateral, the sum of the products of opposite sides equals the product of the diagonals.

Q3: Can this formula be used for any quadrilateral?
A: No, this formula specifically applies to cyclic quadrilaterals where all vertices lie on a circle.

Q4: What are the practical applications of cyclic quadrilaterals?
A: Cyclic quadrilaterals are used in mechanical engineering, architecture, computer graphics, and various geometric constructions.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact for perfect cyclic quadrilaterals, assuming precise input measurements.