Question

In the figure, a circle touches the side $DF$ of $\Delta EDF$ at $H$ and touches $ED$ and $EF$ produced at $K$ and $M$ respectively. If $EK=9$ cm, then the perimeter of $\Delta EDF$ (in cm) is:

• A. $18$
• B. $13.5$
• C. $12$
• D. $9$

Answer 1

The correct option is A $18$

$EK=9$ cm
As length of tangents drawn from an external point to the circle are equal.
$\therefore$ $EK=EM=9$ cm
Also, $DH=DKandFH=FM$ ... (1)
$EK=EM=9$ cm
$\Rightarrow ED+DK=9$ cm and $EF+FM=9$ cm
$\Rightarrow ED+DH=9$ cm and $EF+HF=9$ cm--- (2)
Perimeter of $\Delta EDF=ED+DF+EF$
$=ED+DH+HF+EF$
$=(9+9)$ cm (From equation (2))
$=18$ cm
Therefore, the perimeter $=18$ cm.