Virginia SOL G.PC.4

What SOL G.PC.4 means

Solve problems in the coordinate plane involving equations of circles.

Practice Geometry SOL questions

Free Geometry questions from official Virginia Department of Education released SOL tests — good practice while you work on G.PC.4 and the rest of the course. Pick an answer to check it instantly, or open “Show answer” to review.

1. 1. The perimeter of triangle JKL is 200 centimeters. • JK = 68 centimeters • KL = 62 centimeters Which statement is true about the interior angles of triangle JKL?

   Fm∠L is the greatest of the interior anglesGm∠J is the least of the interior anglesHm∠K is the greatest of the interior anglesJm∠K is the least of the interior angles
   Show answer

   Answer: H — m∠K is the greatest of the interior angles

2. 2. Two triangles, △STW and △XYZ, are shown with corresponding side lengths expressed in terms of x. For △STW, the side lengths are: • ST = x + 5 • TW = 3x + 1 • SW = 3x − 1 For △XYZ, the corresponding side lengths are: • XY = 4x − 3 • YZ = 4x − 5 • XZ = 2x + 1 Which value of x makes △STW ≅ △XYZ?

   A2B3C4D5
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   Answer: A — 2

3. 3. The figure is a regular hexagon with each side measuring 4 inches. Points A, B, C, D, E, and F label consecutive vertices of the hexagon. What is the length of diagonal AC?

   A4√3 in.B8 in.C12 in.D8√3 in.
   Show answer

   Answer: A — 4√3 in.

4. 4. A shed is modeled as a combination of a triangular prism and a rectangular prism. A vertical plane intersects the model and is parallel to the front face of the shed. What is the shape of this cross section?

   FTriangleGPentagonHRectangleJTrapezoid
   Show answer

   Answer: H — Rectangle

→ Take the full free Geometry SOL practice test

Skills you’ll practice for G.PC.4

• Derive the equation of a circle given the center and radius using the Pythagorean Theorem.
• Given a graph or the equation of a circle in standard form, identify the coordinates of the center of the circle.
• Given the coordinates of the endpoints of a diameter of a circle, determine the coordinates of the center of the circle.
• Given a graph or the equation of a circle in standard form, identify the length of the radius or diameter of the circle.
• Given the coordinates of the endpoints of the diameter of a circle, determine the length of the radius or diameter of the circle.
• Given the coordinates of the center and the coordinates of a point on the circle, determine the length of the radius or diameter of the circle.
• Given the coordinates of the center and length of the radius of a circle, identify the coordinates of a point(s) on the circle.
• Determine the equation of a circle given a graph of a circle with a center with coordinates that are integers.
• Determine the equation of a circle given coordinates of the center and a point on the circle.
• Determine the equation of a circle given coordinates of the center and the length of the radius or diameter.
• Determine the equation of a circle given coordinates of the endpoints of a diameter.

Key concepts covered by G.PC.4

• equation of a circle
• center
• radius
• Pythagorean Theorem
• standard form
• circle equation
• center coordinates
• diameter endpoints
• diameter
• point on circle
• circle graph

How to study and practice SOL G.PC.4

Start with a quick diagnostic to see whether G.PC.4 is already solid, then work each skill above with guided notes, flashcards, and SOL-style practice questions. For official released items, see our Virginia SOL practice tests guide and how to study for the SOL test.

→ Take the free Geometry SOL practice test

Related Geometry standards in Polygons and Circles

• G.PC.1 — Prove and justify theorems and properties of quadrilaterals and solve related problems.
• G.PC.2 — Verify relationships and solve problems involving the number of sides and measures of angles of convex polygons.
• G.PC.3 — Solve problems involving properties of circles.

Frequently asked questions about SOL G.PC.4