a circle touches the side \( D F \) of \( \triangle E D F \) at \( H \) and touches \( E D \) an...

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a circle touches the side \( D F \) of \( \triangle E D F \) at \( H \) and touches \( E D \) and \( E F \) (IV) produced at \( K \) and \( M \) respectively. If \( E K=9 \mathrm{~cm} \), then the perimeter of \( \triangle E D F \) is
(a) \( 18 \mathrm{~cm} \)
(b) \( 13.5 \mathrm{~cm} \)
(c) \( 12 \mathrm{~cm} \)
(d) \( 9 \mathrm{~cm} \)
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