**Core Concept**
The otic ganglion is a parasympathetic ganglion located near the foramen ovale, which plays a crucial role in regulating the secretomotor function of the parotid gland. It receives preganglionic parasympathetic fibers from the lesser petrosal nerve and postganglionic fibers from the auriculotemporal nerve.

**Why the Correct Answer is Right**
The lesser petrosal nerve indeed forms the parasympathetic root of the otic ganglion, carrying preganglionic parasympathetic fibers from the glossopharyngeal nerve (cranial nerve IX). These fibers synapse with postganglionic neurons in the otic ganglion, which then transmit signals to the parotid gland through the auriculotemporal nerve, stimulating salivation. The sympathetic root of the otic ganglion is derived from the plexus around the internal carotid artery, which provides a source of postganglionic sympathetic fibers. The otic ganglion is indeed topographically connected to the maxillary division of the trigeminal nerve (cranial nerve V), which provides a pathway for the parasympathetic fibers to reach the parotid gland. However, the nerve to the medial pterygoid is not connected to the otic ganglion.

**Why Each Wrong Option is Incorrect**
**Option A:** This statement is incorrect because the lesser petrosal nerve indeed forms the parasympathetic root of the otic ganglion.
**Option B:** This statement is incorrect because the nerve to the medial pterygoid is not connected to the otic ganglion, which is primarily involved in regulating the parotid gland.
**Option C:** This statement is incorrect because the otic ganglion is not directly connected to the maxillary division of the trigeminal nerve, but rather indirectly through the auriculotemporal nerve.
**Option D:** This statement is incorrect because the sympathetic root of the otic ganglion is indeed derived from the plexus around the internal carotid artery.

**Clinical Pearl / High-Yield Fact**
The otic ganglion is a critical structure in the parasympathetic innervation of the parotid gland, and its dysfunction can lead to salivary gland disorders such as parotid gland hypofunction.

**Correct Answer: B. The statement is False. The nerve to the medial pterygoid is not connected to the otic ganglion.**