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) 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.