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SAT Math skill page

SAT Circle Equations Practice

Connect circle formulas with coordinate geometry so radius, center, and distance questions become easier to spot.

Practice circle equations in Dolphin Try examples
10-15 min practice time 3 examples on page Geometry and Trigonometry
Practice time 10-15 min
On-page examples 3 examples
Best for Geometry and Trigonometry

What this tests

What to know for this SAT skill

Practice examples

Try a few SAT-style questions

Example 1 Easy

A circle has radius 4. What is its diameter?

  1. 2
  2. 4
  3. 8
  4. 16
Show answer and explanation

Answer: 8

The diameter is twice the radius, so 2 x 4 = 8.

Example 2 Medium

The equation of a circle is (x - 3)^2 + (y + 2)^2 = 25. What is the radius?

  1. 3
  2. 5
  3. 10
  4. 25
Show answer and explanation

Answer: 5

In center-radius form, r^2 = 25, so r = 5.

Example 3 Hard

A circle has center (1, 2) and passes through (4, 6). What is the radius?

  1. 3
  2. 4
  3. 5
  4. 7
Show answer and explanation

Answer: 5

Use distance from the center to the point: sqrt((4 - 1)^2 + (6 - 2)^2) = sqrt(9 + 16) = 5.

Avoid these traps

Common mistakes on this skill

Confusing radius and diameter

Diameter is twice the radius. Many SAT answer choices test this swap.

Reading r squared as r

In (x - h)^2 + (y - k)^2 = r^2, the number on the right is r squared.

Missing sign changes in the center

The center of (x - 3)^2 + (y + 2)^2 is (3, -2), not (-3, 2).

Study plan

How to practice this skill in Dolphin

  1. Memorize area, circumference, and center-radius form.
  2. Mark whether the problem asks for radius, diameter, area, or circumference.
  3. For coordinate problems, draw the center and point before using distance.
  4. Check if the final answer should be exact, decimal, or in terms of pi.
Practice circle equations in Dolphin

Related practice

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Skill cluster

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FAQ

Questions about SAT Circle Equations Practice

Are circle equations on SAT Math?

Yes. Circle questions can ask about formulas, coordinate geometry, radius, diameter, or interpreting equation form.

What circle equation should I know?

Know (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center and r is the radius.

How do circle questions connect to distance?

A radius is the distance from the center to a point on the circle, so coordinate circle problems often use the distance formula.