EEdgePrepBETA
Sign inGet started
Math · Geometry

Circles

Work with radius, diameter, circumference, and area, plus the angle relationships formed inside a circle — central angles, inscribed angles, and arcs all connect back to the same 360° whole. Every question comes with a written walkthrough of the relationship used.

Practise circles nowSee sample questions
3
Difficulty tiers
35s
Target pace
52%
Average first-attempt score

What's covered

  • Circumference and area formulas — apply C = 2πr (or πd) and A = πr² correctly, keeping radius and diameter distinct throughout the problem.
  • Arc length — find the fraction of the full circumference that a given central angle sweeps out, using (angle/360°) × 2πr.
  • Sector area — apply the same fractional idea to area: (angle/360°) × πr² for the portion of the circle a sector covers.
  • Central and inscribed angles — a central angle equals the arc it intercepts; an inscribed angle equals half the arc it intercepts.
  • Tangent lines — a tangent line touches a circle at exactly one point and is always perpendicular to the radius drawn to that point.

Where students lose marks

Using diameter where the formula calls for radius

C = 2πr and A = πr² both need the radius specifically — plugging a given diameter directly into either formula without halving it first doubles or quadruples the result.

Forgetting the half in the inscribed angle rule

An inscribed angle is half its intercepted arc, not equal to it — that's the rule for a central angle, a completely different angle sharing the same arc.

Using the wrong angle for a sector's fraction

A sector's arc length and area both scale with its own central angle out of 360°, not with any other angle that happens to appear in the same figure.

Three sample questions

Straight from the bank — one per difficulty tier. Reveal the answer to see the explanation you'd get in a real session.

Sample 01Foundation

A circle has a diameter of 18 cm. Find its circumference. (Use π ≈ 3.14)

Sample 02Core

A sector of a circle with radius 10 cm has a central angle of 72°. Find the arc length. (Use π ≈ 3.14)

Sample 03Advanced

In a circle, an inscribed angle intercepts an arc of 84°. A central angle in the same circle intercepts an arc that is twice as large as the inscribed angle's arc. Find the measure of the central angle.

How to practise this

Circle problems are mostly about tracking which measurement — radius, diameter, arc, or angle — a given formula actually wants, since one wrong substitution changes the whole answer.

Write down radius vs. diameter before choosing a formula

Label every given measurement as either a radius or a diameter before touching a formula. Untimed practice is where that labeling habit sticks.

Then 35 seconds a question

Move to timed sessions once radius/diameter tracking and the central/inscribed angle rules are automatic.

Fold into a mock

Pair circles with area and perimeter in a mock — composite figures frequently combine both.

Stop mixing up the measurements.
Start labeling radius vs. diameter.

  • A formula walkthrough on every item — including which measurement it needs
  • Timed or untimed sessions, any length you like
  • Tracked separately — see your circles accuracy and pace over time
Start practising free

Already have an account? Sign in →

Related Math subtopics

Area and perimeter of basic shapesBasic definitions: angles, lines, linear pairsSupplementary, complementary, congruentTriangle postulates and theoremsAll of Math