so that triangle BDI is isosceles, i. e. we have BD = ID. Similarly, CD = ID. Hence, BD = ID = CD, and the point D is the circumcenter of triangle BIC. Similarly, E and F are the circumcenters of triangles CIA and AIB. [This is an important fact: that the midpoint of the arc BC on the circumcircle of triangle ABC is the circumcenter of triangle BIC.]
upang ang tatsulok BDI ay isosceles, ibig sabihin, kami ay may BD = ID. Katulad nito, CD = ID. Kaya, BD = ID = CD, at ang punto D ay ang circumcenter ng tatsulok BIC.