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From an external point P, two tangents PA and PB are drawn to a circle centred at O. What is true about their lengths PA and PB?
APA is always greater than PB
BPA equals one half of PB
CPA equals PB
DPA equals the radius and PB equals the diameter
Answer & Solution
Correct answer: C. PA equals PB
1. Triangles OAP and OBP share the hypotenuse OP and have right angles at A and B.
2. OA equals OB as both are radii of the same circle.
3. By RHS congruence the two right triangles are congruent.
4. Corresponding sides PA and PB are therefore equal.
5. So the tangent lengths from any external point to a circle are equal.
_Source: SCERT Kerala Std X Mathematics Part-2, Chapter 7 "Tangents" (pp 159-172, 2019 ed.)._
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