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Worksheets›Geometry›Circles›Segments of chords, secants and tangents

Segments of Chords, Secants and Tangents Worksheets

Free printable worksheets with answer keys. Pick a level, preview the questions, then open the sheet to swap or delete any single question.

GeometryCCSS HSG.C.A.2Answer key includedPDF · Print
Open in generatorStart with an easy sheet

Easy: Intersecting chords

  1. 1.Find x.ABCDE888x
  2. 2.Find x.ABCDE333x
  3. 3.Find x.ABCDE233x
  4. 4.Find x.ABCDE1277x
  5. 5.Find x.ABCDE2255x
  6. 6.Find x.ABCDE4612x
Preview shows 6 of 12 questions. Every sheet is new; open it to change any question.

Worksheet variations

When two chords cross inside a circle, the two pieces of one chord multiply to the same product as the two pieces of the other: AE × EB = CE × ED. From a point outside, a tangent squared equals the outside part of a secant times the whole secant: PT² = PA × PB.

EasyFind x.ABCDE10610xIntersecting chordsMediumFind x.PTABx39Tangent and secant: the tangentHardFind x.PTAB93xTangent and secant: the chord

How to solve it: a worked example

Find the value of x.

  1. StartFind x.ABCDE2189x
  2. The products of the chord pieces are equal2 × 18 = 9x
  3. Solve for xx = 369 = 4
  4. Answerx = 4

Common mistakes to watch for

  • Multiplying the outside part by the inside part instead of by the whole secant.
  • Forgetting to square the tangent.
  • Adding the chord pieces instead of multiplying them.

Tip: tick “Step-by-step answer key” in the generator to print each step for marking.

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Arc length and sector areaInscribed and central anglesEquation of a circleAngle pair equationsParallel lines and transversals

FAQ

What is the intersecting chords theorem?

When two chords cross, the products of their parts are equal: AE × EB = CE × ED.

How does the tangent-secant theorem work?

From an outside point, the tangent squared equals the whole secant times its outside part: PT² = PA × PB. Use the whole secant, not just the part inside the circle.

Is every worksheet different?

Yes. Numbers are generated each time, and the answer key is calculated for that sheet. Swap any single question and its answer updates too.

Can I mix segments of chords, secants and tangents with other skills?

Yes. In the generator, add more skills; each gets its own section on the sheet with its own instructions.

Is it free to print?

Yes. Generating and printing from the browser is free with no sign-up. PDF downloads need a free account.