In the figure shown, $${L}$$ is the center of the circle and $$\overline{P Q}$$ is a chord of the circle measuring $$30$$ centimeters (cm). ![](http://admin.getprephub.com/media/editor/t1_20230225220149565923.png) What is the length, in centimeters, of $$P L$$ ?

Given that, ![](http://admin.getprephub.com/media/editor/t1s_20230225220200433990.png) $$\overline{L M}$$ is perpendicular to the chord $$\overline{P Q}$$ and bisects $$\overline{P Q}$$. Therefore, $$\overline{P M}=\frac{30}{2}=15,<L M P=90^{0}$$, In $$\triangle L P M$$ $$P M^{2}+L M^{2}=P L^{2}$$ Putting the values, $$P L^{2}=8^{2}+15^{2}=289=17^{2}$$ Or, $${PL}=17 {~cm}$$

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In the figure shown, ${L}$ is the center of the circle and $\overline{P Q}$ is a chord of the circle measuring $30$ centimeters (cm).

What is the length, in centimeters, of $P L$ ?

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