1. What is the Tangent-Secant Theorem?

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

2. How Does the Calculator Work?

The calculator uses the Tangent-Secant Theorem formula:

Where:

• tangent — Length of the tangent segment from the external point to the circle
• external segment — Length of the part of the secant outside the circle
• whole secant — Total length of the secant from the external point through the circle

Explanation: The calculator can find any missing value when you provide the other two values. It automatically rearranges the formula to solve for the missing variable.

3. Applications of the Theorem

Details: This theorem is useful in geometry problems involving circles, particularly in construction, engineering, and design where circular shapes are involved.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What units should I use?
A: Any consistent unit can be used (cm, inches, etc.) as long as all measurements are in the same unit.

Q2: Does this work for any circle?
A: Yes, the theorem applies to all circles as long as the tangent and secant come from the same external point.

Q3: What if I get an error?
A: Make sure you've entered exactly two values and left one field empty. All values must be positive numbers.

Q4: Can this be used for 3D circles (spheres)?
A: The theorem specifically applies to 2D circles, though similar principles exist for spheres.

Q5: How accurate are the results?
A: Results are accurate to two decimal places, which is sufficient for most practical applications.