Calculator Input
Interactive Graph
Circle mode plots secant power against the tangent squared target. Trig mode plots secant and tangent values over nearby radians.
Formula Used
Circle Secant Tangent Theorem
When one tangent and one secant are drawn from the same external point, the square of the tangent length equals the product of the external secant segment and the whole secant length.
t² = e × w
w = e + i
Here, t is tangent length, e is external secant,
i is internal secant, and w is whole secant.
Trigonometric Secant and Tangent
sec(θ) = 1 / cos(θ)
tan(θ) = sin(θ) / cos(θ)
sec²(θ) - tan²(θ) = 1
How to Use This Calculator
- Select circle theorem mode or trigonometric mode.
- For circle mode, choose the value you want to solve.
- Enter the known lengths in the matching fields.
- Use whole secant or internal secant when solving tangent length.
- For trig mode, enter an angle and select degrees or radians.
- Click Calculate to show the answer above the form.
- Review the steps, graph, and identity check.
- Use CSV or PDF buttons to save your result.
Example Data Table
| Case | External Secant | Internal Secant | Whole Secant | Tangent | Formula Check |
|---|---|---|---|---|---|
| Basic circle theorem | 4 cm | 12 cm | 16 cm | 8 cm | 8² = 4 × 16 |
| Find whole secant | 5 m | 20 m | 25 m | 11.18034 m | 125 = 5 × 25 |
| Find external secant | 3 ft | 9 ft | 12 ft | 6 ft | 36 = 3 × 12 |
| Trig mode | N/A | N/A | N/A | tan(45°) = 1 | sec² - tan² = 1 |
Secant Tangent Calculator Guide
What This Tool Solves
A secant tangent calculator helps solve two common math tasks. The first task comes from circle geometry. A tangent touches a circle at one point. A secant cuts the circle at two points. When both lines start from the same outside point, their lengths follow a powerful theorem. This page uses that theorem to find tangent length, external secant length, internal secant length, or whole secant length.
Why the Theorem Matters
The tangent-secant theorem is useful because it links an outside tangent with a crossing secant. It avoids complex drawing work. You only need enough known lengths. The calculator then creates the missing value and checks the result. This helps students compare the product of secant parts with the square of the tangent.
Advanced Calculation Support
The form supports several solving directions. You can enter external and internal lengths to find the tangent. You can enter tangent and whole secant to find the external part. You can also find the internal part or the whole secant. The tool shows each step in a simple order. This makes the result easier to follow and easier to verify.
Trigonometry Option
The calculator also includes a trigonometric option. It evaluates secant and tangent for a given angle. It supports degrees and radians. It also checks the identity sec squared minus tangent squared equals one. This is helpful when your lesson uses sec and tan as functions.
Graph and Export Benefits
The graph gives a visual check. In circle mode, it compares secant power with the tangent squared target. In trigonometry mode, it plots secant and tangent curves. The CSV export helps with spreadsheets. The PDF export helps with assignments and reports. Use the example table to test values before solving your own problem.
FAQs
1. What is the secant tangent theorem?
It states that tangent squared equals external secant multiplied by whole secant when both lines start from the same external point.
2. What is the external secant?
The external secant is the part outside the circle. It runs from the outside point to the first circle intersection.
3. What is the whole secant?
The whole secant is the full segment from the outside point to the far circle intersection. It includes external and internal parts.
4. How do I find tangent length?
Enter external secant and whole secant, or enter external and internal parts. The calculator applies tangent equals square root of external times whole.
5. Can this calculator solve missing secant parts?
Yes. It can solve external secant, internal secant, and whole secant when enough related values are entered correctly.
6. Why is my result invalid?
An invalid result usually means a negative length, missing required value, or a whole secant smaller than the external part.
7. What does trig mode calculate?
Trig mode calculates secant and tangent for an angle. It also checks the identity sec squared minus tan squared equals one.
8. Can I save the result?
Yes. Use the CSV button for spreadsheet data. Use the PDF button for a clean printable result summary.