Step 1: Objective: The objective is to identify ancient Indian texts pertaining to the art of dance from a given list by examining their content.
Step 2: Textual Analysis:
(A) Saṅgītaratnākara: Composed by Śārṅgadeva in the 13th century, this comprehensive treatise covers Indian classical music and dance. It is a foundational text for Hindustani and Carnatic music and includes a specific chapter on dance (Nartanādhyāya), thus relating to dance.
(B) Nāṭyaśāstra: Attributed to Bharata Muni, this is the oldest and most extensive treatise on Indian performing arts. It thoroughly details drama, music, and dance, serving as the primary source for classical Indian dance forms, hence fundamentally related to dance.
(C) Nṛttasūtra: The name signifies "Aphorisms on Dance" (Nṛtta meaning pure dance). Though less prominent than the Nāṭyaśāstra, references to Nṛttasūtras appear, for instance, in Pāṇini's work. These texts specifically codify dance principles, thereby relating to dance.
(D) Abhinav Candrikā: This text is not a recognized work within the main body of dance literature like the others. While Abhinavagupta authored the significant Nāṭyaśāstra commentary, Abhinavabhāratī, "Abhinav Candrikā" is not among his widely acknowledged dance works and is likely included as a distractor.
Step 3: Conclusion: The Saṅgītaratnākara, Nātyaśāstra, and Nṛttasutra are established texts related to dance. Therefore, the correct selection includes (A), (B), and (C).