TS EAMCET · Maths · Circle
The tangents drawn from a point \((2,-1)\) touch the circle \(x^2+y^2+4 x-2 y+1=0\) at the points A and B. If C is the centre of the circle, then the area (in sq. units) of the triangle ABC is
- A \(\frac{4}{5}\)
- B \(4\)
- C \(8\)
- D \(\frac{8}{5}\)
Answer & Solution
Correct Answer
(D) \(\frac{8}{5}\)
Step-by-step Solution
Detailed explanation
Center \(C=(-2,1)\), radius \(r=\sqrt{2^2+(-1)^2-1}=2\). \(PC=\sqrt{(-2-2)^2+(1-(-1))^2}=\sqrt{16+4}=\sqrt{20}\). \(PA=\sqrt{PC^2-r^2}=\sqrt{20-2^2}=\sqrt{16}=4\). Area \(=\frac{1}{2} r^2 \sin(2\angle ACP) = r^2 \sin(\angle ACP)\cos(\angle ACP)\). Area…
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