Answer:
BC = 13
Explanation:
Triangle ACB is isosceles, so AC = BC = 13.
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The altitude is the perpendicular bisector of the base if and only if the triangle is isosceles. You can prove this, if necessary, by considering common side CD, corresponding angles CDA and CDB, and marked congruent sides DA and DB. These together make triangle CDA congruent to triangle CDB by the SAS postulate. Then CA is congruent to CB by CPCTC.