# If the area of the triangle formed by the x-axis, the normal and the tangent to the circle $\left ( x-2 \right )^{2}+\left ( y-3 \right )^{2}=25$ at the point $\left ( 5,7 \right )$ is A, then 24 A is equal to _______. Option: 1 1225 Option: 2 1255 Option: 3 1125 Option: 4 1555

$(x-2)^{2}+(y-3)^{2}=25$

$x^{2}-4x+y^{2}-6y=12$

Equation of normal $4 x-3 y+1=0$

and equation of tangents $3 x+4 y-43=0$

$\\\text { Area of triangle }=\frac{1}{2}\left(\frac{43}{3}+\frac{1}{4}\right) \times(7) \\ \\=\frac{1}{2}\left(\frac{172+3}{12}\right) \times 7 \\ \\\mathrm{A}=\frac{1225}{24} \\ \\24 \mathrm{~A}=1225$

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