Free Printable WorksheetMathGeometryMath CurriculumG-C.A.3

GEO.130 Use tangent theorems in algebraic problems Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Geometry Math worksheet provides structured practice on GEO.130 Use tangent theorems in algebraic problems. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

GEO.130 Use tangent theorems in algebraic problems - Primary standard selected for prompt fields in this prompt cell: CCSS G-C.A.3. Skill statement in this prompt cell: Select the equation that matches a tangent situation and choose the correct value of the unknown. Associated standards listed with this skill in the curriculum source: CCSS G-C.A.3; FL MA.912.GR.5.3, 6.3; MA G-C.A.3; NY GEO G.G-C.A.3. 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.130 Use tangent theorems in algebraic problems skill assessments:

Problem 1Difficulty: Mastery
A tangent-segment diagram gives two tangents from the same external point: one is (x + 2)2 and the other is 6x + 12. Which equation and valid value of x match the theorem?
A(x + 2)2 + 6x + 12 = 0; x = -2
B(x + 2)2 = 6x + 12; x = 4
C(x + 2)2 = 6x + 12; x = -2 only
Dx + 2 = 6x + 12; x = -2
Solution & Explanation:Set the two tangent lengths equal because they are drawn from the same external point. Solving (x + 2)2 = 6x + 12 gives x = 4 or x = -2, but x = -2 makes the tangent length 0, so the valid value is x = 4.
Problem 2Difficulty: Mastery
The tangent slope is represented by (x + 1)/4, and the radius to the tangent point has slope -2. Which equation matches perpendicular slopes, and what is x?
A(x + 1)/4 + (-2) = 0; x = 7
B(x + 1)/4 = -2; x = -9
C((x + 1)/4)(-2) = 1; x = -3
D((x + 1)/4)(-2) = -1; x = 1
Solution & Explanation:A tangent is perpendicular to the radius, so the slope product is -1. Solving ((x + 1)/4)(-2) = -1 gives x + 1 = 2, so x = 1.
Problem 3Difficulty: Mastery
A final review diagram gives the external secant part and whole secant. From point P, a tangent segment has length x and a secant is drawn through the circle. If the external secant part is 9 and the whole secant is 25, which equation matches the tangent-secant theorem, and what is x?
Ax2 = 9(25); x = 15
Bx2 = 9(16); x = 6
Cx2 = 9 + 25; x = 34
Dx = 9(25); x = 225
Solution & Explanation:For a tangent and secant from the same external point, tangent2 = external part times whole secant. Here x2 = 9(25), so x = 15.

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Frequently Asked Questions

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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.A.3 (Primary standard selected for prompt fields in this prompt cell: CCSS G-C.A.3. Skill statement in this prompt cell: Select the equation that matches a tangent situation and choose the correct value of the unknown. Associated standards listed with this skill in the curriculum source: CCSS G-C.A.3; FL MA.912.GR.5.3, 6.3; MA G-C.A.3; NY GEO G.G-C.A.3. Use this prompt-provided wording as the supporting standard description for this workflow.).

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