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In the given figure, find the $MO\times MS$ of the circle: figure Given that $MP = 16$ and $MQ = 10$

I know I have to prove $\triangle PSM$ and $\triangle NQM$ similar to get ratio.

Lion Heart
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Arya
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    Do you mean you don't know how to prove $\triangle PSM$ and $\triangle NQM$ are similar? They have two equal corresponding angles. – peterwhy Oct 07 '22 at 15:08

1 Answers1

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$\angle P = \angle N$, ($\angle$ 's subtended same segment)

$\angle S=\angle Q=90^ \circ$

$\angle PMS = \angle NMQ$, (3rd $\angle$ of $\triangle$)

$\triangle PMS\sim \triangle NMQ$, (AAA similarity)

$$\frac{PM}{NM}=\frac{MS}{MQ}, \frac{16}{2\times MO}=\frac{MS}{10} $$ $$MO \times MS=80$$

Lion Heart
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