Circle Segment Calculator Guide
Why These Relations Matter
A chord, secant, and tangent problem can look complex at first. Each line has a different role. A chord has both endpoints on the circle. A secant cuts the circle at two points. A tangent touches the circle at one point only. This calculator joins these ideas in one place.
The tool is useful for geometry homework, class notes, design sketches, and test review. It handles intersecting chords, two secants, tangent with secant, equal tangents, chord from radius and angle, and chord from center distance. These cases cover the most common circle power theorems.
How the Logic Works
Circle segment formulas work because products remain balanced. When two chords cross inside a circle, the product of the two parts of one chord equals the product of the other chord parts. When two secants start from the same outside point, each outside part is multiplied by its whole secant. A tangent also follows this pattern. Its squared length equals the outside secant part multiplied by the whole secant.
This makes the calculator helpful beyond direct answers. It shows the chosen formula, the solved unknown, and a check value. You can compare both sides of the equation. That reduces mistakes in signs, units, and segment placement. It also helps students see why the answer is reasonable.
Radius Based Chord Options
The radius tools add another layer. A chord can be found from a radius and a central angle. It can also be found from radius and distance from the center. These options help when the diagram gives circle measures instead of power theorem segments.
Accuracy Tips
Use consistent units for all lengths. Inches, feet, centimeters, and meters all work. Do not mix them in one calculation. For angles, enter degrees. Keep values positive. For distance from center, the distance must be smaller than the radius.
The export buttons help save work. The CSV file is good for spreadsheets. The PDF button is good for notes or quick sharing. Use the example table to test each mode before solving your own diagram.
For best results, label the diagram before entry. Mark outside secant parts first. Then mark inside parts. Put tangent values in the tangent field. Select the missing value in solve menu. Review check line after calculation. It confirms the circle relation.