In a right triangle \( A B C \), right-angled at \( B \), \( D \) is a point on hypotenuse such ...

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In a right triangle \( A B C \), right-angled at \( B \), \( D \) is a point on hypotenuse such that \( B D \perp A C \). If \( D P \perp A B \) and \( D Q \perp B C \) then prove that
(a) \( D Q^{2}=D P \cdot Q C \)
(b) \( D P^{2}=D Q \cdot A P \).
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