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Geometry
# Geometry Warmups

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In the figure above, we have a square and a circle inside a larger square.

Find the radius of the circle, to 3 decimal places.

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Paola Ramírez**

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Find the area (in \(\text{cm}^2\)) of the shaded green square in the blue isosceles right triangle, whose legs have length 6 cm.

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Tan Chee Sen**

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\[ \tan6^{\circ} \times \tan42^{\circ} \times \tan66^{\circ} \times \tan78^{\circ}=\, ?\]

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Sandeep Bhardwaj**

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Rudresh Tomar**

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Three balls are placed inside a cone such that each ball is in contact with the edge of the cone and the next ball. If the radii of the balls are 20 cm, 12 cm, and \(r\) cm from top to bottom, what is the value of \(r\)?

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A K**

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