1. What is the Secant-Tangent Theorem?

The Secant-Tangent Theorem states that when a secant and a tangent meet at an external point, the product of the external segment of the secant and the entire secant length equals the square of the tangent segment.

2. How Does the Calculator Work?

The calculator uses the Secant-Tangent Theorem formula:

Where:

• External — Length of the external part of the secant
• Whole — Length of the entire secant segment
• Tangent — Length of the tangent segment

Explanation: The calculator can find any one missing value when the other two are known.

3. Applications of the Theorem

Details: This theorem is useful in geometry problems involving circles, particularly in construction and design applications where circular elements are present.

4. Using the Calculator

Tips: Enter any two known values (external segment, whole secant, or tangent length) and leave the third field empty or as zero. The calculator will compute the missing value.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between external and whole segments?
A: The external segment is the part of the secant outside the circle, while the whole segment is the entire length of the secant from the external point through the circle.

Q2: Can this be used for two secants?
A: No, this calculator is specifically for secant-tangent combinations. For two secants, you would use the Intersecting Secants Theorem.

Q3: What units should I use?
A: Any consistent length units can be used (cm, inches, etc.), just ensure all measurements are in the same units.

Q4: Does the point have to be outside the circle?
A: Yes, the theorem only applies when the point is outside the circle where a secant and tangent meet.

Q5: Can this be used for 3D geometry?
A: The theorem applies to circles in a plane. For spheres, different geometric principles would apply.