Question

The area of the triangle formed by the tangents from the point $(4,3)$ to the circle $x^2+y^2=9$ and the line joining their points of contact is

• A. $\frac{25}{192}$ sq. units
• B. $\frac{192}{25}$ sq. units
• C. $\frac{384}{25}$ sq. units
• D. None of these

Answer 1

Answer: (B)

$\frac{192}{25}$ sq. units

Area of triangle $=\frac{R{L}^3}{L^2+R^2}$
where R = radius of the circle = 3
L = length of tangent $=\sqrt{S_1}=\sqrt{16+9-9}=4$
Hence area $=\frac{192}{25}sq.$ units