Tangent Secant Theorem Calculator

Tangent Secant Theorem:

\[ \text{Tangent}^2 = \text{secant\_external} \times \text{secant\_full} \]

Result:

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1. What is the Tangent Secant Theorem?

The Tangent Secant Theorem states that when a tangent and secant are drawn from an external point to a circle, the square of the length of the tangent is equal to the product of the lengths of the secant's external part and the whole secant.

2. How Does the Calculator Work?

The calculator uses the Tangent Secant Theorem:

\[ \text{Tangent}^2 = \text{secant\_external} \times \text{secant\_full} \]

Where:

Tangent — Length of the tangent segment from the external point to the circle
secant_external — Length of the external part of the secant (from external point to first intersection with circle)
secant_full — Length of the entire secant (from external point through the circle)

Explanation: The theorem relates these three lengths, allowing you to calculate any one if you know the other two.

3. Importance of the Theorem

Details: This theorem is fundamental in circle geometry and is used in various geometric proofs and constructions. It helps solve problems involving circles, tangents, and secants.

4. Using the Calculator

Tips: Enter any two known values to calculate the third. All values must be positive numbers. The calculator will compute the missing value based on the theorem.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between secant_external and secant_full?
A: The secant_external is the part of the secant from the external point to the first intersection with the circle. The secant_full includes the entire length through the circle to the second intersection point.

Q2: Can this be used for any circle?
A: Yes, the theorem applies to all circles as long as you have a tangent and secant from the same external point.

Q3: What units should I use?
A: You can use any units (cm, inches, etc.) as long as all measurements are in the same units.

Q4: Does the calculator work for degenerate cases?
A: No, all lengths must be positive numbers representing valid geometric configurations.

Q5: How accurate are the results?
A: The results are mathematically exact based on the theorem, though displayed with 4 decimal places for readability.