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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

In a certain right triangle, the hypotenuse equals \((x+z)\) while the other two sides are \((x+y)\) and \((y+z)\) for positive integers \(x, y, z\).

If \(y+4=z\) and \(z>x\) , then compute \(\dfrac{z}{x}\).

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Consider a rectangle which has a diagonal of length 6. If \(P\) is a point on side \(AB\) such that \(\lvert\overline{AP}\rvert=\lvert\overline{AD}\rvert,\) and \( Q\) is a point on the extension of side \(AD\) such that \(\lvert\overline{AQ}\rvert=\lvert\overline{AB}\rvert,\) what is the area of the quadrilateral \(APCQ?\)

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In triangle \(ABC,\) \(AB = AC\) and \(\angle BAC = 100^\circ.\) If \(\overline{AB}\) is extended to \(D\) such that \(AD=BC,\) find \(\angle BCD\) (in degrees).

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