Equal tangents from an external point
Tangents drawn from the same external point to a circle are equal in length.
Practice This ConceptMain explanation
Teacher explanation
If an external point P touches the circle at A and B, then PA = PB. This theorem is extremely important in proofs and length-finding questions. It is not enough to know that the tangents exist; you must also remember that their lengths are equal.
Example
From external point P, if PA and PB are tangents to the circle, then PA = PB.
Simple analogy
Same outside point, same tangent length.
Common confusion
Students sometimes treat tangent lengths from different external points as equal. The theorem works only for tangents from the same external point.
Exam tip
Whenever two tangents start from one outside point, immediately write their lengths equal.
Answer writing and exam use
1-mark use
Write the exact meaning of equal tangents from an external point in one clean line.
2-mark use
Define equal tangents from an external point and add one example or condition.
3-mark use
Explain equal tangents from an external point, show the method or example, and mention the common mistake.
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