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.

$29\ cm$

$\triangle\text{MOP}$ is a right$-$angled triangle.
By Pythagoras theorem,
$MP^2_= MO^2 + OP^2$
$MP^2 = 16^2 + 12^2$
$MP = 20\ cm$
$\triangle\text{NMP}$ 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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