Explanation

(c)
The equation of the tangent at $P(3,\ 4)$ to the circle $x^{2} + y^{2} = 25$is$3x + 4y = 25$, which meets the coordinate axes at $A\left( \frac{25}{3},0 \right)$ and$B\left( 0,\frac{25}{4} \right)$. If $O$ be the origin, then the $\mathrm{\Delta}OAB$ is a right angled triangle with $OA = \frac{25}{3}$ and $OB = \frac{25}{4}$
Area of the $\mathrm{\Delta}OAB = \frac{1}{2} \times OA \times OB = \frac{1}{2} \times \frac{25}{3} \times \frac{25}{4} = \frac{625}{24}$