In the given figure, O is a point inside a such that =90^ ,OM=16c… - Vidyadip

MCQ

In the given figure, $O$ is a point inside a $\triangle\text{MNP}$ such that $\angle\text{MOP}=90^\circ,\text{OM}=16\text{cm}$ and $OP = 12\ cm$. If $MN = 21\ cm$ and $\angle\text{NMP}=90^\circ$ then $NP = ?$

A
$25\ cm$
✓
$29\ cm$
C
$33\ cm$
D
$35\ cm$

✓

Answer

Correct option: B.

$29\ cm$

$\triangle MOP$ is a right$-$angled triangle.
By Pythagoras theorem,
$M P^2=M O^2+O P^2$
$M P^2=16^2+12^2$
$M P=20 cm$
$\triangle NMP$ is a right$-$angled triangle.
By PYthagoras theorem,
$N P^2=21^2+20^2$
$N P^2=4411+400$
$N P=29 \ cm$

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