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TS EAMCET · Maths · Circle

The area (in sq units) of the triangle formed by the tangent, normal at \((1, \sqrt{3})\) to the circle \(x^2+y^2=4\) and the \(X\)-axis, is

  1. A \(4 \sqrt{3}\)
  2. B \(\frac{7}{2} \sqrt{3}\)
  3. C \(2 \sqrt{3}\)
  4. D \(\frac{1}{2} \sqrt{3}\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(2 \sqrt{3}\)

Step-by-step Solution

Detailed explanation

The equations of the tangent and normal to the circle \(x^2+y^2=4\) at \(P(1, \sqrt{3})\) are \( x+\sqrt{3} y=4 \text { and } y=\sqrt{3} x \) The tangent meets \(X\)-axis at \(A(4,0)\). \(\therefore\) Area of \(\triangle O A P=\frac{1}{2} \times 4 \times \sqrt{3}=2 \sqrt{3}\) sq…