Tangents, Chords and Position of a Point
A point lies inside, on or outside a circle according to the sign of S1, and the tangent at a point on the circle is given by T = 0.
What is Tangents, Chords and Position of a Point?
A point lies inside, on or outside a circle according to the sign of S1, and the tangent at a point on the circle is given by T = 0.
Key formula / rule: Length of the tangent from an external point is √(S1).
Key points
- Classify the position of a point relative to a circle.
- Derive the equation of a tangent or chord of contact using T = 0.
Common exam trap
Applying the tangent-length formula to an interior point.
Definitions
- Term
Tangents, Chords and Position of a Point
- Meaning
A point lies inside, on or outside a circle according to the sign of S1, and the tangent at a point on the circle is given by T = 0.
- Term
Tangents, Chords and Position of a Point — explanation
- Meaning
The single expression S1 answers position, power of a point and tangent length questions. The T = 0 shortcut writes tangent and chord-of-contact equations without differentiation.
Learning objectives
Classify the position of a point relative to a circle.
Derive the equation of a tangent or chord of contact using T = 0.
Formulae
- Key point
Length of the tangent from an external point is √(S1).
- Key point
T = 0 gives the tangent at a point on the circle and the chord of contact from an outside point.
- Key point
The condition for a line to touch a circle is that the distance from the centre equals the radius.
Prerequisites
MAT-U3-SL-T1-S2-C1
Common mistakes
Applying the tangent-length formula to an interior point.
Using T = 0 as the tangent when the point is not on the circle without recognising it as a chord of contact.
Keywords
Tangents
Chords
Position
Point
Practice preview
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