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Question

In the given figure, ray $$PQ$$ touches the circle at point $$Q$$. $$PQ = 12, PR = 8$$, find $$PS$$ and $$RS$$. 

1853692_4c4b5be3d14c417d9cc2f51722654dfe.png


Solution

Using tangent secant segments theorem we have
$$PQ^{2}=PR \times PS$$
$$\Rightarrow (12)^{2}=8 \times PS$$
$$\Rightarrow PS=\frac{144}{8}=18$$ units
$$\therefore RS=PS-PR=18-8=10$$ units

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