Valmiki Ramayana, Ayodhya-kanda, Sarga 112
The exact passage where Bharata asks for the padukas and Lord Rama wears, removes and gives them to his brother.
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Bharata receives Lord Rama’s padukas
Valmiki Ramayana 2.112.21
आधिरोहाऽर्य पादाभ्यां पादुके हेमभूषिते। एतेहि सर्वलोकस्य योगक्षेमं विधास्यतः॥
Bharata asks Rama to place His feet upon the gold-adorned sandals, which will secure the welfare of the world.
Valmiki Ramayana 2.112.22
सोऽधिरुह्य नरव्याघ्रः पादुके ह्यवरुह्य च। प्रायच्छत्सुमहातेजा भरताय महात्मने॥
Rama puts on the sandals, removes them and gives them to noble Bharata.