Geometry Warmups

Geometry Warmups: Level 3 Challenges


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.

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

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

The 5 circles have the same size. If the side of the large square is 1, what is the radius of each circle (to 3 decimal places)?

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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