In the figure given below (not to scale), \( D \) is a point on the circle with centre \( A \) a...

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In the figure given below (not to scale), \( D \) is a point on the circle with centre \( A \) and \( C \) is a
P point on the circle with centre \( B . \overline{A D} \perp \overline{B D} \) and \( \overline{B C} \perp \overline{C A} \). Then which of the following is true?
(a) \( B D=A C \), when \( A D=B C \)
(b) \( B D=A C \), when \( \overline{A D} \| \overline{B C} \)
(c) Both (a) and (b)
(d) \( B D=A C \) is always true
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