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# Geometric Inequalities

Given 5 sticks of length 1, 3, 5, 9, and 10, how many distinct triangles can be formed? Learn the techniques and develop an intuition for working with 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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