Find the average area of an inscribed triangle in the unit circle.Assume that each vertex of the triangle is equally likely to be at any point of the unit circle and that the location of one vertex does not affect the likelyhood the location of another in any way.
(note that the maximum area is achieved by the equilateral trian

In the figure (see attachment) there are infinitely many circles approaching the vertices of an equilateral triangle, each circle touching other circles and sides of the triangle. If the triangle has sides of length 1, find the total area occupied by the circles.

Using the fact that the centroid of a triangle lies at the intersection of the triangle's medians, which is the point that lies one-third of the way from each side toward the opposite vertex. Find the centroid of the triangle whose vertices are (0,0), (a,0) and (0,b). Assume a > 0 and b >0.

Use strong induction to show that when a convex polygon P with consecutive vertices VI, V2, ... , Vn is triangulated into n - 2 triangles, the n - 2 triangles can be numbered 1, 2, ... , n - 2 so that Vi is a vertex of triangle i for i = 1,2, ... , n - 2.

4. What are the projections of the point (2, 3, 5) on the xy, yz-, and xz-planes? Draw a rectangular box with the origin and (2, 3, 5) as opposite vertices and with its face parallel to the coordinate planes. Label all vertices of the box. Find the length of the diagonal of the box.
8. Find the lengths of the sides of the tr

The circumscribed circle is the circle passing through the three vertices of a triangle ABC. Assume the following results from geometry. The perpendicular bisectors of the sides of a triangle meet in a point O that is the center of the circumscribed circle.
a) According to a theorem from geometry, the measure of the angle

1. Find the area of the triangle.
2. There is a shaded triangular prism 6in x 8in x 11in with a rectangle solid 3in x 4in x 11in not shaded. Find the volume of the shaded area.
3. Given the graph, name an edge that is a bridge, if any.
4. Find the area in meters of a trapezoid with a height of 4 m and bases of 8 m and