How it works
This circle geometry test has 54 review questions: parts of a circle, arcs and central angles, inscribed angles, chords, tangents and secants, and arc length, sector area and circle equations, each with the working.
Read the full guide
Five sets
Parts of a circle is the vocabulary. Arcs and Inscribed angles solve for angles and for x. Chords, tangents and secants uses the segment products and the right angle at a tangent. The last set measures arcs and sectors and reads circle equations.
Before the test
Practice brings a missed question back until you get it right. After a round, Print lists its questions: remove one, add more up to all 54, and tick With answer key.
- An inscribed angle is half its arc; a central angle equals its arc.
- A tangent meets the radius at 90°, so look for a right triangle and use Pythagoras.
- Chords that cross: multiply the two parts of each chord and set the products equal.
Questions and answers
What is the inscribed angle theorem?
An inscribed angle is half the central angle that stands on the same arc, so it is half the arc's measure. An angle inscribed in a semicircle is therefore 90°.
How do you find the length of an arc?
Take the fraction of the circle, the central angle over 360°, and multiply by the circumference 2πr. A 60° arc of a circle with radius 6 is (60/360) × 12π = 2π.
What is the equation of a circle?
(x − h)² + (y − k)² = r², where (h, k) is the centre and r the radius. Watch the signs: (x + 1)² means h = −1.