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In figure, \( \mathrm{AD} \) is a median of \( \triangle \mathrm{ABC} \) and \( \mathrm{AE} \perp \mathrm{BC} \). If \( \mathrm{BC}=\mathrm{a}, \mathrm{CA}=\mathrm{b}, \mathrm{AB}=\mathrm{c}, \mathrm{AD}=\mathrm{p}, \mathrm{AE}=\mathrm{h} \) and \( \mathrm{DE} \) \( =\mathrm{x} \). Which of the following is/are correct?
a. \( b^{2}=p^{2}+a x+\frac{a^{2}}{4} \)
b. \( c^{2}=p^{2}-a x+\frac{a^{2}}{4} \)
c. \( \mathrm{b}^{2}+\mathrm{c}^{2}=2 \mathrm{p}^{2}+\frac{1}{2} \mathrm{a}^{2} \)
d. \( b^{2}-c^{2}=2 a x \)
\( \mathrm{P} \)
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