Free Printable WorksheetMathGeometryMath CurriculumG-C.A.3

GEO.120 Tangents to circles Worksheet

Download our free printable Geometry Math worksheet on GEO.120 Tangents to circles. Ideal for classroom practice, homeschool learning, independent homework, and standardized test preparation. Available in both print-ready PDF and editable DOCX formats.

Choose your preferred download format:

100% Free • No registration or login required • Instant file access

Prefer interactive practice with instant grading and explanations?Practice Tangents to circles Online

Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Geometry Math worksheet provides structured practice on GEO.120 Tangents to circles. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

GEO.120 Tangents to circles - Primary standard selected for prompt fields in this prompt cell: CCSS G-C.A.3. Skill statement in this prompt cell: Select the correct tangent property and determine an unknown angle or segment length involving tangents and radii. 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.120 Tangents to circles skill assessments:

Problem 1Difficulty: Mastery
Which pair of conditions is enough to prove that TP is tangent to circle O at T?
AT lies on circle O, and OT is perpendicular to TP
BOP is longer than OT, and T is outside the circle
COT and TP have equal lengths
DP lies on circle O, and OP passes through T
Solution & Explanation:A line is tangent at T when it touches the circle at T and is perpendicular to the radius drawn to T. Therefore T must lie on the circle and OT must be perpendicular to TP.
Problem 2Difficulty: Mastery
Two tangents PA and PB touch a circle at A and B. If angle APB = 120 degrees, what are central angle AOB and angle AOP?
AAOB = 60 degrees and AOP = 30 degrees
BAOB = 120 degrees and AOP = 60 degrees
CAOB = 60 degrees and AOP = 60 degrees
DAOB = 180 degrees and AOP = 90 degrees
Solution & Explanation:The central angle is supplementary to the tangent angle: AOB = 180 - 120 = 60 degrees. OP bisects central angle AOB, so angle AOP = 30 degrees.
Problem 3Difficulty: Mastery
Circle O has radius 15. Two tangents from P have total length 72. Find OP.
A36
B39
C51
D72
Solution & Explanation:The tangents from P are congruent, so each is 72/2 = 36. In right triangle OAP, OP = sqrt(152 + 362) = sqrt(1521) = 39.

Want more practice questions with step-by-step guidance?

Practice All Questions Online

Frequently Asked Questions

Common questions about printing, using, and solving this worksheet

QHow do I download and print this GEO.120 Tangents to circles worksheet?

Click either the "Download PDF" or "Download DOCX" button at the top of the page. You can print the PDF directly from your browser or edit the DOCX file in Microsoft Word or Google Docs to tailor the questions to your students.

QIs this GEO.120 Tangents to circles worksheet free for teachers and homeschoolers?

Yes! All learning materials, worksheets, and practice resources on Free K12 Practice are 100% free for teachers, students, parents, tutors, and homeschooling families for non-commercial educational use. No account or subscription is required.

QCan students practice GEO.120 Tangents to circles online with instant feedback?

Yes! In addition to this printable worksheet, students can practice GEO.120 Tangents to circles interactively on our platform with automated grading, instant score tracking, and detailed step-by-step solutions.

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 correct tangent property and determine an unknown angle or segment length involving tangents and radii. 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.).

Related Geometry Math Resources

Continue learning with complementary skill worksheets and online practice