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Circles — 25-Question Test
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Formula Reference Sheet
This chapter
Chords, tangents & power of a point
| Perpendicular from centre bisects chord | OM ⊥ AB ⇒ AM = MB |
|---|---|
| Chord length from distance d to centre | chord = 2√(r² − d²) |
| Tangent length from external point P | PT = √(OP² − r²) |
| Two intersecting chords | PA × PB = PC × PD |
| Secant–secant from external P | PA × PB = PC × PD |
| Tangent–secant from external P | PT² = PA × PB |
Angles in a circle
| Angle at centre vs circumference | ∠centre = 2 × ∠circumference (same arc) |
|---|---|
| Angle in a semicircle | Angle on a diameter = 90° |
| Cyclic quadrilateral opposite angles | ∠A + ∠C = ∠B + ∠D = 180° |
| Alternate segment theorem | angle between tangent & chord = inscribed angle in alternate segment |
| Angles in the same segment | equal (subtend the same arc) |
| Exterior angle of cyclic quad | = interior opposite angle |
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