# Equal Areas In Equal Time

Calculus Level 4

A square $$5 \times 5$$ is positioned in the $$4^\text{th}$$ quadrant intersecting part of a circle of radius $$5$$ and centered at $$(-2, 0)$$. The square is rotated counter-clockwise about the origin.

Through what angle (in degrees) does the square have to be rotated until $$\frac 1 2$$ of its area intersects with the circle?

[Answer to nearest 3 decimal places]

×