Answer:
5 miles
Explanation:
We are looking at triangles LCM and OGM.
Point M is the midpoint of segments LO and CG.
That makes segments CM and GM congruent (side).
Then angles CML and GMO are congruent since they are vertical angles (angle).
Finally, segments LM and OM are also congruent because of the midpoint (side).
By SAS, triangles LCM and OGM are congruent.
Then by CPCTC, segments LC and OG are congruent.
Since OG = 5 miles, then LC = 5 miles.
Answer: 5 miles