...that Orange County has nearly 700 miles of paths and trails that are open to mountain bikes?

One of Orange County's many bike paths.
This includes fire road, singletrack, and double track trails, with 158 miles of trails and fire roads in Cleveland National Forest, nearly 200 miles on OC Parks land and 66 miles between Chino Hills and Crystal Cove State Parks. Municipal riding areas like the Fullerton Loop, San Clemente Singletracks, Las Ramblas and others also contain many more miles of trails and fire roads. 

Just over 60 multi-use paved and unpaved paths covering 422 miles connect parks and off-road riding networks, including the Peters Canyon and Mountains to Sea trails that run from Tustin/Irvine to Newport Beach and the Aliso Creek Bikeway, which links Lake Forest, Mission Viejo, Laguna Hills and other communities with Aliso and Woods Canyon Wilderness Park to the south, and Whiting Ranch, the Luge and Live Oak Canyon to the north. The Arroyo Trabuco and Tijeras Creek networks connect Rancho Santa Margarita and O'Neill Park with Ladera Ranch, San Juan Capistrano and other South County communities and destinations, and the 30-mile Santa Ana River Trail runs from the Corona area to the coast. 

Like many urban areas in the U.S., Orange County's cycling infrastructure has room for improvement, but for a relatively small and densely populated county, these trail totals are significant. Trailforks.com and MTB Project are excellent resources for exploring area bikeways and planning safe routes to trailheads and other destinations. and Google Maps also does a good job of providing bike-friendly routes for commuting and getting around on two wheels.