Grades 11-12 Video Solutions 2025-2025_11-12

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The problem involves finding the maximum sum of radii \( R1 + R2 + R3 + R4 \) for disks centered at specified points such that they touch but do not overlap. By establishing inequalities (e.g., \( R1 + R2 \leq 1 \), \( R2 + R3 \leq 2 \), \( R3 + R4 \leq 3 \)), it is deduced that the combined radius \( R1 + R2 + R3 + R4 \) must be \( \leq 4 \). The answer choices C, D, and E exceed this maximum, leaving B (4) as the only valid solution. A combination such as \( R1 = 0.5, R2 = 0.5, R3 = 1.5, R4 = 1.5 \) satisfies the conditions. Thus, the answer is B.