As shown in the figure, △ ABC and △ DBC, the angle BAC = angle BDC = 90 °, O is the midpoint of BC (1) △ AOD is isosceles triangle? Why?

Right triangle, hypotenuse center line = 1 / 2 * hypotenuse
It can be proved by adding parallelogram

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15. In triangle ABC, bisectors be and CD of angle ABC and angle ACB intersect at point O. if angle a = 60 °, what is the relationship between BC, CE and BD
16. As shown in the figure, in the triangle ABC, the angle a = 60 degrees. The bisectors BD and CE of the triangle ABC intersect at point F. if be = 4 and CD = 2, find the length of BC
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