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TS EAMCET · Maths · Circle

Let \(\mathrm{P}\) and \(\mathrm{Q}\) be two external points of the circle \(S \equiv x^2+y^2-a^2=0\). Let the chord of contact of the point \(\mathrm{P}\) with respect to the circle \(S=0\) pass through Q. If \(l_1\) and \(l_2\) are the lengths of the tangents drawn from \(\mathrm{P}\) and \(\mathrm{Q}\) to the circle \(S=0\), then \(\mathrm{PQ}=\)

  1. A \(\sqrt{l_1+l_2}\)
  2. B \(\frac{l_1+l_2}{2}\)
  3. C \(\sqrt{l_1^2+l_2^2}\)
  4. D \(\sqrt{l_1^2-2 l_1+l_2^2-2 l_2}\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(\sqrt{l_1^2+l_2^2}\)

Step-by-step Solution

Detailed explanation

Given circle \(S \equiv x^2+y^2=a^2\) with two external points \(\mathrm{P}\) and Q. Let point \(\mathrm{P}\) be \((\mathrm{h}, \mathrm{k})\) and point \(\mathrm{Q}\) be \((\mathrm{p}, \mathrm{q})\). Equation of chord of contacts of tangent from \(\mathrm{P}\) is…