A line segment of length 2 moves in the xy-plane such that it always touches both the coordinate axes (see the image below). Find the area of the region swept out by the line segment.
16-4*pi Since we have tangents at the points where the curves meet the axes, curves can only be quarters of the circle radius 2. This is further supported by x^2+y^2=4 which is true for any position of the line. One quarter of the shaded area= area of square side 2 minus one quarter of the area of the circle radius 2 i.e. (4-pi). Hence the total shades area =16-4*pi
A unit sphere (radius = 1) is out on a flat plane in the rain. Find the side length of the largest cube that can hide underneath it and not get wet.
A circle is inscribed inside a trapezium ABCD such that it touches all 4 sides of this trapezium.
Given that the area of this trapezium is 4 and the diameter of the circle is 1, find the value of the ratio AB/CD.
A cube is sliced into halves in such a way that the cut is a regular hexagon. What is the angle (in degrees) between the plane of the cut and the base of the cube?
In a semicircle, the circular segment ADB is folded along AB to make the circular segment ATB. The point T is tangent to the diameter and divides the diameter into lengths of 4 and 2. What is the length of AB?
A small circle is contained inside a quarter circle and tangent to one of its sides. A line segment is constructed to be tangent to the small circle and perpendicular to the other side of the quarter circle. If the line segment has length equal to 12, what is the area shaded in blue, equal to the area of the quarter circle minus the small circle?
