In the given figure, $O$ is the center. $P M$ and $M Q$ are tangents to the circle at points $P$ and $Q$ respectively. Find the value of $O M$ .

8 c m

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6 c m

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10 c m

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None of the above

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Solution

The correct option is D None of the above
$P M$ is tangent to the circle at $P$

$∴ ∠ O P M = 90^{o}$ ....... ( $∵$ tangent is perpendicular to the radius of a circle)

By using Pythagoras theorem,
${O M}^{2} = {P M}^{2} + {P O}^{2}$

${O M}^{2} = {P M}^{2} + {O P}^{2} = 100 + 64 = 164$

$∴ O M = \sqrt{164} c m$ .

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In the given figure, O is the center. PM and MQ are tangents to the circle at points P and Q respectively. Find the value of OM.

The correct option is D None of the abovePM is tangent to the circle at P∴∠OPM=90o ....... (∵ tangent is perpendicular to the radius of a circle)By using Pythagoras theorem,OM2=PM2+PO2OM2=PM2+OP2=100+64=164∴OM=√164cm.

In the given figure, $O$ is the center. $P M$ and $M Q$ are tangents to the circle at points $P$ and $Q$ respectively. Find the value of $O M$ .