By Saqib Iqbal Ahmed NEW YORK (Reuters) - The dollar fell across the board on Tuesday, hitting a four-year low against the euro, as investors firmed bets for a Federal Reserve interest rate cut this week. The euro rose by 0.9% higher to $1.1867, its highest level since September 2021. The U.S. dollar index, which tracks the dollar against a basket of six major currencies, was 0.7% lower at 96.636, its lowest since July 1. The dollar, which had steadied in recent months following a significant drop earli ...