Why is Point J is also equidistant from points F and C to the following. Answer in one sentence

Question

Explanation
Recognize $$\overline{GH}$$ is the perpendicular bisector of $$\overline{FC}$$
Identify $$\overline{FJ} \cong \overline{CJ}$$ due to the perpendicular bisector
$$\angle IJF$$ and $$\angle IJC$$ are right angles
$$\angle IJF \cong \angle IJC$$ by the Right Angles Congruence Theorem
$$\overline{IJ} \cong \overline{IJ}$$ (Reflexive Property)
Prove $$\triangle IJF \cong \triangle IJC$$ by the Hypotenuse-Leg Congruence Theorem
$$\overline{IF} \cong \overline{IC}$$ by Corresponding Parts of Congruent Triangles Theorem

Answer 1

Point J is equidistant from points F and C because it lies on the perpendicular bisector of segment FC, creating congruent segments FJ and CJ through the properties of congruent triangles.