In the given figure, \( O P \) is the perpendicular bisector of the line RQ, TS \( \perp \) OP a...

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In the given figure, \( O P \) is the perpendicular bisector of the line RQ, TS \( \perp \) OP and the line segment TQ intersects \( \mathrm{OP} \) at \( \mathrm{U} \). Prove that \( \frac{1}{\mathrm{OS}}+\frac{1}{\mathrm{OP}}=\frac{2}{\mathrm{OU}} \)
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