Free Printable WorksheetMathGeometryMath CurriculumG-C.B.5

GEO.133 Solve mixed circle problems with arcs, angles, and sectors Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Geometry Math worksheet provides structured practice on GEO.133 Solve mixed circle problems with arcs, angles, and sectors. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

GEO.133 Solve mixed circle problems with arcs, angles, and sectors - Primary standard selected for prompt fields in this prompt cell: CCSS G-C.B.5. Skill statement in this prompt cell: Select the correct multi-step setup and choose the correct numeric result for a combined circle problem. 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; CCSS SMP.1; NY HS MP; MA 2017 SMP; TEKS §111.41(b)(2) Process; WIDA 2020-Language Expectations. 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.133 Solve mixed circle problems with arcs, angles, and sectors skill assessments:

Problem 1Difficulty: Mastery

Two secants from an exterior point form a 45-degree angle. The larger intercepted arc is 210 degrees in a circle of radius 18. Which setup and result correctly find the smaller sector area and perimeter?

Asmall=210-45=165; area=297pi/2 and perimeter=33pi/2+36

Bsmall=210+2(45)=300; area=270pi and perimeter=30pi+36

Csmall=45; area=81pi/2 and perimeter=9pi/2+36

D45=(210-small)/2, so small=120; area=(120/360)pi(18²)=108pi and perimeter=(120/360)2pi(18)+2(18)=12pi+36

Solution & Explanation:Exterior secants use half the arc difference. Solve 45=(210-small)/2 to get small=120 degrees. The smaller sector area is 108pi and its perimeter is arc length 12pi plus two radii, 36.

Problem 2Difficulty: Mastery

Sector A is in a circle of radius 12 and is intercepted by an inscribed angle of 30 degrees. Sector B is in a circle of radius 8 and has central angle 90 degrees. Which setup and conclusion correctly compare their arc lengths?

ASector A length=2pi and Sector B length=4pi; Sector B is longer

BSector A length=4pi and Sector B length=2pi; Sector A is longer

CSector A central angle=60, so length=(60/360)2pi(12)=4pi. Sector B length=(90/360)2pi(8)=4pi; the arc lengths are equal

DSector A central angle=30, so length=2pi. Sector B central angle=90, so length=4pi; Sector B is longer

Solution & Explanation:The inscribed angle for Sector A intercepts a 60-degree arc, giving length 4pi. Sector B's 90-degree arc with radius 8 also has length 4pi, so the arc lengths are equal.

Problem 3Difficulty: Mastery

A sector has area 80pi square units in a circle whose total area is 180pi square units. Which setup and result correctly find the central angle and arc length of the sector?

Asector fraction=4/9, so theta=80; arc length=8sqrt(5)pi/3

Bsector fraction=80/180=4/9, so theta=(4/9)360=160; r=6sqrt(5); arc length=(160/360)2pi(6sqrt(5))=16sqrt(5)pi/3

Csector fraction=80/360, so theta=80; arc length=8sqrt(5)pi/3

Dsector fraction=180/80, so theta=810; arc length=27sqrt(5)pi

Solution & Explanation:The sector is 80pi/180pi=4/9 of the circle, so theta=160 degrees. Since pi r²=180pi, r=6sqrt(5). Arc length is (160/360)2pi(6sqrt(5))=16sqrt(5)pi/3.

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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.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 multi-step setup and choose the correct numeric result for a combined circle problem. 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; CCSS SMP.1; NY HS MP; MA 2017 SMP; TEKS §111.41(b)(2) Process; WIDA 2020-Language Expectations. Use this prompt-provided wording as the supporting standard description for this workflow.).