With the addition of the ­iPad mini, Apple offers touchscreen devices in three sizes. Now rival Google is doing the same, introducing a 10-inch tablet, an upgraded 7-inch tablet, and a new smartphone.

Introduced Monday, the Nexus 10, which Google developed with Samsung, is the company’s first tablet that competes directly with Apple’s 9.7-inch iPad. Most significantly, it undercuts the iPad’s price: A Nexus 10 with Wi-Fi and 16 gigabytes of storage costs $400, compared with $500 for an equivalent iPad. Google did not say whether a model with cellular data would be available.