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 tangent's length equals the product of the entire secant length and its external part.

2. How Does the Calculator Work?

The calculator uses two forms of the Tangent-Secant Theorem:

Where:

• \( \text{Tangent} \) — Length of the tangent segment
• \( \text{Secant} \) — Entire length of the secant segment
• \( \text{Chord} \) — Length of the chord inside the circle (external part of secant)
• \( \text{Power} \) — Power of the point relative to the circle

Explanation: You can calculate either the tangent length given secant and chord, or the power given tangent length.

3. Importance of Tangent-Secant Calculations

Details: These calculations are fundamental in circle geometry, used in construction, engineering, and various geometric proofs involving circles.

4. Using the Calculator

Tips: Either enter tangent length to calculate power, or enter both secant and chord lengths to calculate tangent. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between secant and chord?
A: A secant is a line that intersects the circle at two points, while a chord is the segment of the secant that lies inside the circle.

Q2: Can I calculate chord length if I know tangent and secant?
A: Yes, rearrange the formula: Chord = Secant - (Tangent²/Secant)

Q3: What is the "power" of a point?
A: The power of a point relative to a circle is the product of the lengths of the two segments from the point to the circle along any line through it.

Q4: Does this work for any point outside the circle?
A: Yes, as long as you can draw a tangent and secant from that point to the circle.

Q5: How accurate are these calculations?
A: The calculations are mathematically exact, though practical measurements may have precision limitations.