\( \mathrm{ABD} \) is a triangle in which \( \angle \mathrm{DAB}=90^{\circ}, \mathrm{AC} \perp \...

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\( \mathrm{ABD} \) is a triangle in which \( \angle \mathrm{DAB}=90^{\circ}, \mathrm{AC} \perp \mathrm{BD} \).
Which of the following is/are correct?
a. \( \mathrm{AB}^{2}=\mathrm{BC} \times \mathrm{BD} \)
b. \( \mathrm{AC}^{2}=\mathrm{BC} \times \mathrm{DC} \)
c. \( \mathrm{AD}^{2}=\mathrm{BD} \times \mathrm{AC} \)
d. \( \mathrm{DB}^{2}=\mathrm{AD} \times \mathrm{CD} \)
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