NY State Math Geometry Circles. Practice it free.

Per the NYSED Geometry Educator Guide blueprint, Circles (G-C) is 2%–8% of credit, covering theorems about circles and arc lengths and areas of sectors. This Geometry reporting domain maps to 2 practice skills and 8 representative questions from the playable bank.

GeometryG-C2 mapped skills
What the test measures

Circles skills

  1. Understand and apply theorems about circles

  2. Find arc lengths and areas of sectors of circles

Standards basis

New York State Learning Standards / New York State Next Generation Learning Standards (NGLS) — New York

How the NY State Math reports it

New York’s Grades 3–8 math tests and Regents math exams are state-developed assessments rather than a shared national framework. The grades 3–8 exams are aligned to New York State learning standards, and the Regents math sequence includes Algebra I, Geometry, and Algebra II, with the June 2026 Algebra II exam explicitly based on the New York State Next Generation Learning Standards.

Blueprint & weighting

Grades 3–8: the official page and the retrieved administration guide describe item/credit structure and timing, but no published domain-by-domain blueprint weighting was located in the primary sources used here. Regents (high school): NYSED publishes a per-conceptual-category 'percent of test by credit' blueprint for each course in its Educator Guides. Algebra I — Number & Quantity 4%–10%, Algebra 48%–61%, Functions 24%–32%, Statistics & Probability 7%–15%. Geometry (single conceptual category, by domain) — Congruence (G-CO) 27%–34%, Similarity, Right Triangles, & Trigonometry (G-SRT) 29%–37%, Circles (G-C) 2%–8%, Expressing Geometric Properties with Equations (G-GPE) 12%–18%, Geometric Measurement & Dimensions (G-GMD) 2%–8%, Modeling with Geometry (G-MG) 8%–15%. Algebra II — Number & Quantity 4%–8%, Algebra 30%–39%, Functions 38%–45%, Statistics & Probability 14%–22%.

Practice by skill

Topics mapped to this domain

Advanced area formulas

Grade 1015 questions

Perimeter and arc length

Grade 1015 questions
Try it now

8 free questions · 0/0 correct

Practice playeasy

A right triangle has legs 66 and 88. What is its area?

Area =12×6×8=24= \dfrac{1}{2} \times 6 \times 8 = 24.

Practice playeasy

A rectangular garden measures 1515 by 66. How many units of fencing are needed to go all the way around it?

P=2(15+6)=2⋅21=42P = 2(15 + 6) = 2 \cdot 21 = 42.

Practice playeasy

Find the area of a sector with radius 44 and central angle 60°60°. Use π=3\pi = 3.

Sector area =60360×πr2=60360×3×16=8= \dfrac{60}{360} \times \pi r^2 = \dfrac{60}{360} \times 3 \times 16 = 8.

Practice playeasy

Find the arc length of a 90°90° arc on a circle with radius 66. Use π=3\pi = 3.

L=90360×2πr=14×2×3×6=9L = \dfrac{90}{360} \times 2 \pi r = \dfrac{1}{4} \times 2 \times 3 \times 6 = 9.

Practice playeasy

A triangle has sides 55, 1212, and 1313. What is its area?

This is a right triangle (55-1212-1313). Area =12×5×12=30= \dfrac{1}{2} \times 5 \times 12 = 30.

Practice playeasy

Find the arc length of a 180°180° arc on a circle with radius 33. Use π=3\pi = 3.

L=180360×2πr=12×2×3×3=9L = \dfrac{180}{360} \times 2 \pi r = \dfrac{1}{2} \times 2 \times 3 \times 3 = 9.

Practice playeasy

A rhombus has diagonals of length 1010 and 1212. What is its area?

Area =12×10×12=60= \dfrac{1}{2} \times 10 \times 12 = 60.

Practice playeasy

Find the arc length of a 90°90° arc on a circle with radius 22. Use π=3\pi = 3.

L=90360×2πr=14×2×3×2=3L = \dfrac{90}{360} \times 2 \pi r = \dfrac{1}{4} \times 2 \times 3 \times 2 = 3.

Keep practicing

Turn circles into game time.

The NY State Math placement starts with this test's real coverage map and finds the right difficulty.

Batting Cage game coverBatting CagePlay →Blossom Leap game coverBlossom LeapPlay →Buzzer Beater game coverBuzzer BeaterPlay →Minecart Junction game coverMinecart JunctionPlay →
Related Common Core standards
HSG.C.B.5
The same skills on other tests
ATLASDC CAPEMCAPMO MAP
Source and test overview
All NY State Math prepOfficial test source
Reporting categories

More Geometry domains

CongruencePer the NYSED Geometry Educator Guide blueprint, Congruence (G-CO) is 27%–34% of credit, covering transformations in the plane, congruence in terms of rigid motions, geometric theorems, and constructions.8 QsPractice →Similarity, Right Triangles, & TrigonometryPer the NYSED Geometry Educator Guide blueprint, Similarity, Right Triangles, & Trigonometry (G-SRT) is 29%–37% of credit, covering similarity transformations, theorems involving similarity, right-triangle trigonometry, and trigonometry of general triangles.8 QsPractice →Expressing Geometric Properties with EquationsPer the NYSED Geometry Educator Guide blueprint, Expressing Geometric Properties with Equations (G-GPE) is 12%–18% of credit, covering conic-section equations and coordinate proofs.8 QsPractice →Geometric Measurement & DimensionsPer the NYSED Geometry Educator Guide blueprint, Geometric Measurement & Dimensions (G-GMD) is 2%–8% of credit, covering volume formulas and relationships between two- and three-dimensional objects.8 QsPractice →Modeling with GeometryPer the NYSED Geometry Educator Guide blueprint, Modeling with Geometry (G-MG) is 8%–15% of credit, applying geometric concepts in modeling situations.8 QsPractice →