Circle Theorems Flashcards

Grade 10 · Math · Flashcards

Key theorems, formulas, and vocabulary for circles to build fluency and recall.

Flashcards

Inscribed Angle Theorem

An inscribed angle = ½ × (intercepted arc). Equivalently, it is half the central angle on the same arc.

Angle in a Semicircle

An inscribed angle that intercepts a diameter (semicircle) is always 90°.

Angles Subtended by Same Arc

All inscribed angles that intercept the same arc are equal to each other.

Cyclic Quadrilateral — Opposite Angles

Opposite angles of a cyclic quadrilateral are supplementary (add to 180°).

Cyclic Quadrilateral — Exterior Angle

An exterior angle of a cyclic quadrilateral equals the interior opposite angle.

Intersecting Chords Theorem

If chords AB and CD intersect at P inside the circle: AP × PB = CP × PD.

Power of a Point (secant-secant)

External point P: PA × PB = PC × PD where A,B and C,D are the intersection pairs.

Power of a Point (tangent-secant)

External point P: PT² = PA × PB where PT is the tangent length and A,B are secant intersections.

Tangent-Chord Angle

The angle between a tangent and a chord at the point of tangency = ½ × (intercepted arc).

Tangent from External Point

Two tangents drawn from the same external point are equal in length.

Perpendicular from Centre to Chord

The perpendicular from the centre of a circle to a chord bisects that chord.

Equal Chords

Equal chords are equidistant from the centre, and chords equidistant from the centre are equal.

Angle at Centre vs. Circumference

The angle at the centre is twice the angle at the circumference when both subtend the same arc.

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