Geometry & Trigonometry • 15% of test
Circles
Select your difficulty level to start practicing. We recommend mastering each level before moving to the next.
Beginner5 Sets
Beginner Practice
Start here to build your foundation. Clear problems and straightforward calculations.
Target Score
400-550
Intermediate5 Sets
Intermediate Practice
Level up with more complex equations and multi-step problems.
Target Score
550-700
Advanced3 Sets
Advanced Practice
Master the hardest concepts. Complex word problems and abstract applications.
Target Score
700-800
What is Circles?
Circle questions test the standard equation, arc length, sector area, and relationships between central angles and inscribed angles.
Step-by-Step Strategy
⚠️ Common Traps to Avoid
Frequently Asked Questions
How do I find center and radius from the equation?
In (x-h)² + (y-k)² = r², center is (h,k) and radius is r. Note the sign changes!
What's the difference between arc and chord?
Arc is the curved distance along the circle. Chord is the straight line connecting two points.
How do I convert to standard form?
Complete the square for both x and y terms, then compare to standard form.
What's the inscribed angle theorem?
An inscribed angle is half the central angle that subtends the same arc.
Can I use Desmos for circles?
Yes! Type the equation to graph the circle and find intercepts or intersections.
How common are circle questions?
Expect 1-2 per test. Focus on arc/sector relationships in our <a href='/math'>Geometry & Trigonometry category</a>.
What is the 'General Form' of a circle?
x² + y² + Dx + Ey + F = 0. You must complete the square for x and y to find the center (h,k) and radius r.
How do I find the area of a 'Ring'?
Subtract the inner circle's area from the outer circle's area: Area = πR² - πr².
What is the relationship of 'Radians' and 'Degrees'?
360° = 2π radians. To convert degrees to radians, multiply by π/180. The SAT often uses radians in 2026.
What is the 'Arc Length' formula in radians?
s = rθ, where θ is the central angle in radians. This is simpler than the degree-based version.
How do I find 'Sector Area' in radians?
Area = ½r²θ, where θ is the central angle in radians. Note the coefficient of 1/2.
What is a 'Tangent' line to a circle?
A line touching the circle at exactly one point. It is always perpendicular to the radius at that specific point.
What is the 'Chord' length relationship?
Often solved by creating a right triangle using the radius and the perpendicular distance from the center to the chord.
What if a circle is 'Inscribed' in a square?
The diameter of the circle is equal to the side length of the square. Radius is half the side.
What if a circle is 'Circumscribed' around a square?
The diagonal of the square equals the diameter. Master complex shapes in <a href='/math/geometry/advanced'>Advanced Geometry practice</a>.