The CD must be a bad arc, the title is fine, and the picture can be drawn. Draw a picture yourself first. The heart is the angle of the bisector of three internal angles. The following are proved separately.

1. Angle FCA= Angle ECB = Angle AFC= Angle BEC, so Angle FAE= Angle FBE.

Triangle AFC is similar to BCE, FC: CE = AC: BC, so triangle FCE is similar to ACB.

According to the relationship between the central angle and the circular arc central angle, angle FDC= 1/2 angle FAE, angle EDC= 1/2 angle FBE, so angle FDC= 1)

Because the triangle FCE is similar to ACB, the angle FEC= the angle ABC, and AB is perpendicular to CD by using the relationship between the central angle and the circular arc central angle.

There is angle CED= angle ABC, so angle FEC= angle ABC (2)

Similarly provable angle EFC= angle CFD (3)

So point C is the heart of triangle DEF.