Chord Secant Tangent Calculator

Check circle segment relations with very clear steps. Compare chord, secant, and tangent cases easily. Download structured results for classwork, tutoring, and practice today.

Calculator Form

Example Data Table

Mode Known values Missing value Expected result
Intersecting chords b = 6, c = 4, d = 9 a 6
Two secants e1 = 3, i1 = 5, e2 = 4 i2 2
Tangent and secant external = 4, inside = 5 tangent 6
Two tangents first tangent = 12 second tangent 12
Chord from radius and angle radius = 10, angle = 60° chord 10
Chord from radius and distance radius = 13, distance = 5 chord 24

Formula Used

The calculator uses circle power theorems and chord geometry.

How to Use This Calculator

  1. Select the circle relation that matches your diagram.
  2. Choose the value you want to solve.
  3. Enter all required known values for that selected relation.
  4. Use the same length unit for every length value.
  5. Enter central angles in degrees.
  6. Press calculate to see the answer above the form.
  7. Use CSV or PDF export when you need saved work.

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.

FAQs

What is a chord?

A chord is a straight segment with both endpoints on a circle. A diameter is the longest possible chord.

What is a secant?

A secant is a line or segment that passes through a circle at two points. Outside secant problems often use external and whole lengths.

What is a tangent?

A tangent touches a circle at exactly one point. It does not pass through the circle.

Which formula handles two crossing chords?

Use a × b = c × d. Each product comes from the two parts of one chord.

How do I enter a secant whole length?

Do not enter the whole length directly. Enter the external part and inside part. The calculator builds the whole secant automatically.

Can this calculator solve for an angle?

Yes. Select the radius and angle chord mode. Then choose central angle as the missing value.

Can I use meters or inches?

Yes. Any length unit works. Use the same unit for every length in one calculation.

Why is my chord distance invalid?

The center distance must be smaller than the radius. A chord cannot sit outside the circle.

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Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.