2. In the picture below, suppose that \( O \) is the center of the circle (so \( \overline{B D} \) is a diameter), \( \overline{A B} \) and \( \overline{A C} \) are tangent to the circle at points \( B \) and \( C \) (respectively), and \( \overline{C E} \) is perpendicular to \( \overline{B D} \). (a) Prove that \( \overline{A O} \) is the perpendicular bisector of \( \overline{B C} \). (b) Prove that \( \triangle B E C \sim \triangle A B O \).
Added by Mackenzie S.
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