The correct answer is option 3, Dwarasamudra. The Hoyasala dynasty was a powerful medieval Indian dynasty that ruled over parts of present-day Karnataka, India. Dwarasamudra, also known as Halebidu, was the capital city of the Hoyasalas. It was established by King Vishnuvardhana in the 12th century and remained the seat of power for the dynasty for several decades. Dwarasamudra was renowned for its architectural brilliance, particularly the Hoysaleswara Temple, which is a UNESCO World Heritage Site and one of the finest examples of Hoysala architecture. The city flourished as a center of art, culture, and trade during the reign of the Hoyasalas. It was later captured and destroyed by the Delhi Sultanate in the 14th century.