Proof
STATEMENTS REASONS
| AM = CM | chords intersecting congruent arcs are congruent |
| angle A = angle C | angles intercepting same arc are congruent |
| AB = DC | given in construction |
| triangle ABM = triangle CDM | SAS |
| MB = MD | CPCTC |
| triangle BMD is isosceles | Definition of isosceles triangle |
| triangle BFM = triangle DFM | HL |
|
BF = FD AB + BF = FD + DC FD + DC = FC AB + BF = FC |
CPCTC Substition Substitution Substitution |