In Fig. \( \quad \mathrm{D} \) is a point on hypotenuse \( \mathrm{AC} \) of \( \triangle \mathr...

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In Fig. \( \quad \mathrm{D} \) is a point on hypotenuse \( \mathrm{AC} \) of \( \triangle \mathrm{ABC} \), such that \( \mathrm{BD} \perp \mathrm{AC}, \mathrm{DM} \perp \mathrm{BC} \) and \( \mathrm{DN} \perp \mathrm{AB} \). Prove that :
(i) \( \mathrm{DM}^{2}=\mathrm{DN} \cdot \mathrm{MC} \)
(ii) \( \mathrm{DN}^{2}=\mathrm{DM} \cdot \mathrm{AN} \)
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