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# Geometry Warmups

Mathematics is filled with shapes that are kaleidoscopic in variety. Wielded since ancient times, the power of geometry helps us examine and measure these shapes.

# Geometry Warmups: Level 3 Challenges

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

Find the area (in $$\text{cm}^2$$) of the shaded green square in the blue right triangle.

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

The 5 circles have the same size. If the side of the large square is 1, what is the radius of each circle?

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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