Free Printable WorksheetMathGeometryMath CurriculumG-C.B.5

GEO.131 Apply chord and secant segment relationships Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Geometry Math worksheet provides structured practice on GEO.131 Apply chord and secant segment relationships. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

GEO.131 Apply chord and secant segment relationships - Primary standard selected for prompt fields in this prompt cell: CCSS G-C.B.5. Skill statement in this prompt cell: Select the correct segment-product relationship and compute the missing segment length. Associated standards listed with this skill in the curriculum source: CCSS G-C.B.5; FL MA.912.GR.6.4; MA G-C.B.5; NY GEO G.G-C.B.5. Use this prompt-provided wording as the supporting standard description for this workflow.

Whether you are an educator preparing classroom handouts, a tutor reinforcing weekly topics, or a parent supporting homeschool learning, this printable resource gives students the deliberate practice required to achieve subject fluency and master state standards.

Grade

Geometry

Subject

Math

Domain

Math Curriculum

Formats

PDF & DOCX

Sample Practice Problems

Preview the types of problems and questions covered in this worksheet

Below are sample questions representative of the exercises included on this worksheet and related GEO.131 Apply chord and secant segment relationships skill assessments:

Problem 1Difficulty: Mastery

An online design draft labels two secants from exterior point P. Secant 1 has exterior length 2x and interior length 18. Secant 2 has exterior length x + 3 and interior length 27. Which relationship correctly finds x?

A2x*(2x + 18) = (x + 3)*(x + 30); x = 5

B2x*18 = (x + 3)*27; x = 81/9

C2x + 18 = x + 3 + 27; x = 12

D(2x)² = (x + 3)²; x = 3

Solution & Explanation:Each secant product is exterior times whole. The first whole length is 2x + 18, and the second whole length is x + 3 + 27 = x + 30. So 2x(2x + 18) = (x + 3)(x + 30). Expanding gives 3x² + 3x - 90 = 0, or x² + x - 30 = 0, so x = 5.

Problem 2Difficulty: Mastery

Two chords intersect. One chord is split in a 3:5 ratio, and its shorter segment is 9. The other chord has one segment 12 and the missing segment x. Which relationship and value of x are correct?

A3*5 = 12*x; x = 5/4

B9 + 15 = 12 + x; x = 12

C15*12 = 9*x; x = 20

D9*15 = 12*x; x = 45/4

Solution & Explanation:A 3:5 ratio with shorter segment 9 means the scale factor is 3, so the other segment is 15. The chord theorem gives 9*15 = 12*x. Thus 135 = 12x and x = 45/4.

Problem 3Difficulty: Mastery

From point P, two secants and a tangent are drawn to the same circle. Secant 1 has exterior length 4 and whole length 64. Secant 2 has exterior length 8 and whole length 32. The tangent has length x. Which relationship and value of x are correct?

Ax = 4*64 = 8*32; x = 256

Bx² = 4*64 = 8*32; x = 16

Cx² = 4 + 64 = 8 + 32; x = sqrt68

D4*32 = 8*64; x cannot be found

Solution & Explanation:Both secant products match: 4*64 = 256 and 8*32 = 256. The tangent also satisfies x² = 256, so x = 16.

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QWhat grade level and standards does this worksheet align with?

This worksheet is designed specifically for Geometry Math students. It aligns with educational standard G-C.B.5 (Primary standard selected for prompt fields in this prompt cell: CCSS G-C.B.5. Skill statement in this prompt cell: Select the correct segment-product relationship and compute the missing segment length. Associated standards listed with this skill in the curriculum source: CCSS G-C.B.5; FL MA.912.GR.6.4; MA G-C.B.5; NY GEO G.G-C.B.5. Use this prompt-provided wording as the supporting standard description for this workflow.).