How did Dixit find out that Madhavrao Deshpande was in town? Who connected them?

The crucial connection between Dixit and Madhavrao was made by Nanasahib Panshe and Appasahib Gadre. As detailed in Chapter 51, Madhavrao had just arrived in Nagar and was getting down from his carriage when Panshe and Gadre happened to pass by, using the exhibition as a pretext for their walk. They were overjoyed to see Madhavrao, whom they recognized as 'the priest of Shirdi,' and immediately realized he was the perfect person to accompany Dixit. They approached Madhavrao, told him about Dixit's eagerness to visit Shirdi, and directed him to Mirikar's house. Simultaneously, they informed Dixit of Madhavrao's arrival, which instantly vanished his worries.