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Given a triangle with side lengths of 5, 12, and 14, is the largest angle in the triangle acute, right, or obtuse? Geometric knowledge helps us deduce much about triangles from limited information. See more

If \(x=\sqrt{6}\) and \(y=\sqrt{10}\) in right triangle \(\triangle ABC\) shown in the diagram above, what is the length of \(\overline{AC} ?\)

**Note:** The above diagram is not drawn to scale.

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What is the value of \(N\)?

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In the figure above, if \(l_1=10,\) \(l_2=8\) and \(\alpha=\beta={56}^\circ,\) what is the value of \(x ?\)

**Note:** The above diagram is not drawn to scale.

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As shown in the above diagram, Raj folded a rectangular paper \(ABCD\) with side length \(\overline{AD} = 5 \) in such a way that vertex \(D\) falls on side \(AB\) and is labeled point \(F.\) If the length of \(\overline{AF}\) is \(2,\) what is the length of \( \overline{DE}?\)

**Note:** The above diagram is not drawn to scale.

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