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Circumcentre of  a triangle is equidistant from the vertices.that is here bd=cd=ad .with the provided data we can say that when we join ad, bd,cd, these line act as the circumradius of circumcircle . the angle of circle is divided into three that is 120* .in this case we can observe that in the first sub triangle formed (adb)ad=ab.it is similar in all three triangles.these are isosceles triangle. so the base angle are equal that is 30* in <abd,<bad,<bcd,<cbd,<acd,<cad, this proves that bd and cd are bisectors of angle ABC AND ACB.
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