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AP EAMCET · Maths · Circle

The area of the triangle (in sq. units) formed by the tangents drawn from \(P(4,4)\) to the circle \(S \equiv x^2+y^2-2 x-2 y-7=0\) and the chord of contact of \(P\) with respect to \(S=0\) is

  1. A 4.5
  2. B 8.1
  3. C \(6.75\)
  4. D \(1.5\)
Verified Solution

Answer & Solution

Correct Answer

(A) 4.5

Step-by-step Solution

Detailed explanation

\(R = \sqrt{1^2+1^2-(-7)} = 3\) \(t^2 = 4^2+4^2-2(4)-2(4)-7 = 16+16-8-8-7 = 9\) \(L^2 = (4-1)^2+(4-1)^2 = 3^2+3^2 = 18\) \(\text{Area} = \frac{R t^3}{L^2} = \frac{3 \cdot (9)^{3/2}}{18} = \frac{3 \cdot 27}{18} = \frac{81}{18} = 4.5\)