Circles
Intersection of circles
Grade 11

Question:

<p>Find the number of ordered pairs (a, b) that satisfy all three circle inequalities with centers at (1, 1), (1, 2), and (2, 1).</p>

Step-by-Step Solution

Key Concept: Find the intersection of three circular regions and count the integer lattice points within that region.
<p><strong>Step 1:</strong> Points satisfying the inequalities are common to all 3 circles given by centers (1, 1), (1, 2), and (2, 1).</p><p><strong>Step 2:</strong> The integer lattice points in the intersection region are: (1, 1), (2, 2), (2, 3), (3, 2), and two other points.</p><p><strong>Step 3:</strong> Number of ordered pairs (a, b) = 6</p>
Correct Answer: 6

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