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Angle between the tangents to the circle $x^2+y^2=25 x^2$ from the point $(1,7)$ is
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$\frac{\pi}{2}$
$\begin{aligned} & \mathrm{OP}=5 \sqrt{2} \\ & \mathrm{OT}=5 \\ & \mathrm{PT}=\sqrt{\mathrm{OP}^2-\mathrm{OT}^2}=5 \\ & \Rightarrow \angle \mathrm{OPT}=45^{\circ} \\ & \Rightarrow \angle \mathrm{TPT}^{\prime}=2 \angle \mathrm{OPT}=2 \times 45^{\circ}=90^{\circ}\end{aligned}$
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