Free Printable WorksheetMathGeometryMath CurriculumG-CO.D.12-13

GEO.125 Construct tangents and inscribed and circumscribed circles Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Geometry Math worksheet provides structured practice on GEO.125 Construct tangents and inscribed and circumscribed circles. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

GEO.125 Construct tangents and inscribed and circumscribed circles - Primary standard selected for prompt fields in this prompt cell: CCSS G-CO.D.12-13. Skill statement in this prompt cell: Select the correct construction steps or final diagram that constructs a tangent line or an inscribed or circumscribed circle. Associated standards listed with this skill in the curriculum source: CCSS G-CO.D.12-13; FL MA.912.GR.5.1-5.3; TEKS §111.41(c); MA G-CO.D.12-13; 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.125 Construct tangents and inscribed and circumscribed circles skill assessments:

Problem 1Difficulty: Mastery

A construction goal says: build the incircle of triangle ABC, then draw tangents from an exterior point P to that incircle. Which plan is correct?

AConstruct the circumcenter with perpendicular bisectors, draw the circumcircle, then use side AB as both tangents.

BPick any point inside the triangle as center, draw a circle, then connect P to two random points on it.

CConstruct medians to find G, draw a circle through the vertices, then draw lines from P through G.

DConstruct the incenter I with angle bisectors, draw the incircle using a perpendicular radius to a side, then use the diameter-circle construction with center I and exterior point P.

Solution & Explanation:This composite task first requires the incircle center and radius, then the standard external-point tangent construction using the incircle's center and point P.

Problem 2Difficulty: Mastery

A construction goal says: first build the circumcircle of triangle ABC, then draw a tangent to that circle at vertex A. Which complete sequence is correct?

AConstruct angle bisectors to find incenter I, draw the incircle, draw IA, then construct the perpendicular to IA through I.

BConstruct medians to find centroid G, draw a circle through side midpoints, then draw a line through A parallel to BG.

CConstruct perpendicular bisectors to find circumcenter O, draw the circle through A, B, and C, draw OA, then construct the perpendicular to OA through A.

DDraw any circle through A, draw any line that touches it in the sketch, and label it tangent.

Solution & Explanation:The circumcircle center comes from perpendicular bisectors. Once radius OA is known, the tangent at A is perpendicular to OA at A.

Problem 3Difficulty: Mastery

Triangle ABC has a circumcircle, and point P is one of the triangle's vertices on that circle. Which plan constructs the tangent to the circumcircle at P?

AConstruct the incenter I using angle bisectors, draw IP, then use IP as the tangent line.

BConstruct the circumcenter O using perpendicular bisectors, draw OP, then construct the line through P perpendicular to OP.

CDraw the side of the triangle opposite P and call it the tangent.

DConstruct a median to P and use it as the tangent.

Solution & Explanation:The tangent to a circle at a point is perpendicular to the radius to that point.

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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-CO.D.12-13 (Primary standard selected for prompt fields in this prompt cell: CCSS G-CO.D.12-13. Skill statement in this prompt cell: Select the correct construction steps or final diagram that constructs a tangent line or an inscribed or circumscribed circle. Associated standards listed with this skill in the curriculum source: CCSS G-CO.D.12-13; FL MA.912.GR.5.1-5.3; TEKS §111.41(c); MA G-CO.D.12-13; 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.).