Question 92

In the given figure. a smaller circle touches a larger circle at P and passes through its centre 0. PR is a chord of length 34 cm. then what is the length (in cm) of PS?

Solution

In the given figure, in $$\triangle$$ PSO and $$\triangle$$ PRQ

=> $$\angle PSO=\angle PRQ$$ (angles of the semi circle)

and $$\angle SPO=\angle RPQ$$ (common angle)

=> $$\triangle$$ PSO $$\sim$$ $$\triangle$$ PRQ

Thus, $$\frac{PS}{PR}=\frac{OP}{QP}$$

=> $$\frac{PS}{34}=\frac{1}{2}$$

=> $$PS=\frac{34}{2}=17$$ cm

=> Ans - (B)

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