1. What is the Tangent-Secant Theorem?

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

2. How Does the Calculator Work?

The calculator uses the Tangent-Secant Theorem formula:

Where:

• external - The length of the external part of the secant
• whole - The total length of the secant segment
• tangent - The length of the tangent segment

Explanation: You can calculate any one of these values if you know the other two. The calculator automatically determines which value to calculate based on which two values you provide.

3. Applications of the Theorem

Details: This theorem is useful in geometry problems involving circles, particularly in construction and design problems where tangent and secant relationships need to be calculated.

4. Using the Calculator

Tips: Enter any two known values (external segment, whole secant, or tangent length) and the calculator will compute the third value. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

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

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

Q3: What if I know different combinations of segments?
A: The calculator automatically detects which value to compute based on the two values you enter.

Q4: Can this be used for 3D geometry?
A: The theorem specifically applies to circles in plane geometry.

Q5: How accurate are the results?
A: Results are accurate to two decimal places for practical use.