In a triangle \( P Q R, P Q=Q R . A \) and \( B \) are the mid-points of \( \overline{Q R} \) an...

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In a triangle \( P Q R, P Q=Q R . A \) and \( B \) are the mid-points of \( \overline{Q R} \) and \( \overline{P R} \) respectively. A circle passes through \( P, Q, A \) and \( B \). Then which of the following is necessarily true?
(a) \( \triangle P Q R \) is equilateral
(b) \( \triangle P Q R \) is right isosceles
(c) \( P Q \) is a diameter
(d) Both (a) and (c)
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