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

$29\ cm$

$\triangle\text{MOP}$ is a right $-$ angled triangle.
By Pythagoras theorem,
${MP}^2={MO}^2+{OP}^2$
$M P^2=16^2+12^2$
$MP = 20\ cm$
$\triangle\text{NMP}$ is a right $-$ angled triangle.
By Pythagoras theorem,
$NP^2= 21^2+ 20^2$
$NP^2= 441 + 400$
$NP = 29\ cm$

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