<p>Find the number of ordered pairs <code>(a, b)</code> that satisfy all three circle inequalities with centers at <code>(1,1)</code>, <code>(1,2)</code>, and <code>(2,1)</code>.</p>
Step-by-Step Solution
Key Concept: Find integer lattice points that lie in the intersection of regions defined by three circular inequalities.
<p><strong>Step 1:</strong> The points satisfying all three circle inequalities are those in the common region</p><p><strong>Step 2:</strong> Check integer points: <code>(1,1), (1,2), (2,1), (2,2), (2,3), (3,2)</code></p><p><strong>Step 3:</strong> All six points satisfy the given inequalities</p><p><strong>Step 4:</strong> Number of ordered pairs <code>(a, b) = 6</code></p>
Correct Answer: 6