options: Apply geometric concepts in modeling situations.

Use coordinates to prove simple geometric theorems algebraically.

Graph points on the coordinate plane to solve real-world and mathematical problems.

Classify two-dimensional figures into categories based on their properties.

Understand and apply theorems about circles.

Reason with shapes and their attributes.

Understand congruence in terms of rigid motions.

Apply trigonometry to general triangles.

Solve real-world and mathematical problems involving area, surface area, and volume.

Translate between the geometric description and the equation for a conic section.

Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.

Prove theorems involving similarity.

Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.

Find arc lengths and areas of sectors of circles.

Define trigonometric ratios and solve problems involving right triangles.

Understand congruence and similarity using physical models, transparencies, or geometry software.

Make geometric constructions.

Draw, construct, and describe geometrical figures and describe the relationships between them.

Analyze, compare, create, and compose shapes.

Understand and apply the Pythagorean Theorem.

Explain volume formulas and use them to solve problems.

Understand similarity in terms of similarity transformations.

Draw and identify lines and angles, and classify shapes by properties of their lines and angles.

Experiment with transformations in the plane.

Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres).

Prove geometric theorems.

Visualize relationships between two-dimensional and three-dimensional objects.
problem_activity: Task
This problem examines equations defining different circles in the $x$-$y$ plane.
Use the Pythagorean theorem to
find an equation in $x$ and $y$ whose solutions are the points on the circle  of radius 2 with center $(1,1)$  and explain why it works.
Suppose $r$ is a positive number and $(a,b)$ a point in the plane.
Use the Pythagorean theorem to
find an equation in $x$ and $y$ whose solutions are the points on the circle of radius $r$ with center $(a,b)$ and explain why it works.


correct_option_index: 9