Circle Geometry Study Guide: 74 Flashcards from Arc Length to the Inscribed Angle Theorem
Master circle geometry with deck OP2222: arc length, sector area, inscribed angle and tangent theorems, circle equations, plus the cards you should fix first.
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Circles look like the easy chapter: one constant, two formulas, done. Then a problem asks for the angle between a tangent and a chord, or for an arc length given in degrees, and it falls apart. Deck OP2222 — Circles: Area, Circumference, Arcs & Theorems (74 cards, free on Flip It) covers that whole chapter, but it is built like a dictionary: it defines nearly everything and computes almost nothing — 4 cards out of 74 actually run a calculation. Treat it as vocabulary, then build the drill yourself.
Study this deck: Circles: Area, Circumference, Arcs & Theorems
1 / 10Circle
Tap the card for the answer · swipe right if you knew it, left if not
The five blocks, in deck order
- Cards 1–27, the parts: radius, diameter, circumference, disc, chord, arc, semicircle, sector, segment, tangent, point of tangency, secant, annulus, concentric circles, plus Euclid's definition and the Greek kuklos.
- Cards 28–36, radians: the radian itself, 2π for a full turn, π for 180°, arc length s = rθ, sector area A = ½r²θ, central angle.
- Cards 37–51, the theorems: inscribed angle, Thales, intersecting chords (ab = cd), tangent-chord angle, tangent-secant, power of a point, equal chords equidistant from the centre, the perpendicular from the centre bisecting a chord.
- Cards 52–60, coordinates: x² + y² = r², (x − a)² + (y − b)² = r², parametric and polar forms, the unit circle.
- Cards 61–74, properties: all circles similar, infinite symmetry axes, three non-collinear points, circumcircle, cyclic quadrilaterals, the isoperimetric inequality, squaring the circle.
Ten real cards
| Front | Back |
|---|---|
| Formula for circumference | C = 2πr or C = πd |
| If a circle has radius 3, what is its area? | 9π ≈ 28.27 (A = π(3)²) |
| Sector | A region bounded by two radii and the arc between them (like a pizza slice) |
| Segment | A region bounded by a chord and the arc between its endpoints |
| Arc length formula | s = rθ, where θ is the angle in radians |
| Inscribed angle theorem | An inscribed angle is half the central angle subtending the same arc |
| Thales' theorem for circles | An angle inscribed in a semicircle is a right angle |
| Intersecting chords theorem formula | If chords intersect at P dividing into a,b and c,d, then ab = cd |
| Tangent-secant theorem | (tangent)² = (near part of secant) × (whole secant) |
| General equation of a circle | (x − a)² + (y − b)² = r², where (a,b) is the center |
Two fixes that make it exam-ready
Write the degree versions. The deck gives arc length and sector area in radians only. Homework hands you 72° or 135°, and converting every time is where marks vanish. Add two cards: s = (θ/360) × 2πr and A = (θ/360) × πr². Same gap at card 19 — segment is defined but never gets an area formula while sector gets one at card 34. The missing back is A = ½r²(θ − sin θ).
Repair four cards first. Card 74 asks for the shortest distance from a point to a circle and answers with a direction ("along the line connecting the point to the center") instead of the number, which is |d − r|. Cards 8 and 9 state the same fact about π twice; cards 42 and 43 state the intersecting-chords theorem twice, once in words and once as ab = cd — keep the version carrying the formula and suspend the other. And note that segment here means circular segment, never the line segment of card 14; the deck reuses the word without warning, and so do exam papers.
Search deck code OP2222 in the Flip It library to start reviewing.
More geometry: Master Triangles & Polygons · Learn 3D Geometry: Volume, Surface Area and the Platonic Solids
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