Algebra
# Geometric Inequalities

If \(AB = 4\), \(AC = 5\), \(BD = 8\), \(CD = 15\), and \(AD\) is a positive integer, find \(AD\).

Over all real numbers \(x\), find the minimum value of \( \sqrt{(x+6)^2+25} + \sqrt{(x-6)^2+121} \).

**Details and assumptions**:

Brilli the ant is completely confined to the surface of the cube. She can't move inside or outside the cube.

Give your answer in degrees.

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