\( \mathrm{D} \) is a point on the side \( \mathrm{BC} \) of \( \triangle \mathrm{ABC} \) such t...

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\( \mathrm{D} \) is a point on the side \( \mathrm{BC} \) of \( \triangle \mathrm{ABC} \) such that \( \angle \mathrm{ADC}=\angle \mathrm{BAC} \). Prove that \( \frac{\mathrm{CA}}{\mathrm{CD}}=\frac{\mathrm{CB}}{\mathrm{CA}} \) or, \( \mathrm{CA}^{2}=\mathrm{CB} \times \mathrm{CD} \).
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