Proof involving circle

Here is the question to prove: Given a circle with radius Q, and a point on the circle R and considering a circle with diameter QR. Let a line go through R and intersect the smaller circle at S and the larger circle at T. Construct a diagram and prove that RS=ST.

Some simple euclidean proofs

Here is the question to prove: There are two questions here. 1. I need to see a construction and proof. Given a quadrilateral EFGH so that all four sides are congruent to a circle. Prove that EF+GH=EH+FG 2. Prove that a perpendicular bisector of a chord in a circle is a diameter.

Geometry problem

Prove that if opposite angles are supplementary, then the quadrilateral can be inscribed in a circle.

Proof involving equilateral triangle

I need to see a construction and proof. Let (triangleDEF) be equilateral triangle and Q is a point inside.Prove that the sum of the three distaces from Q to each side is equal to the altidude DD'.

Collineation

What are the fixed points of a translation T? A fixed point is a point that is not moved by a given collineation, i.e. P = TP

Plucker coordinate

1. Let d = (1, 2, -2), m = (-8, 5, 1) (a) Check that d and m are orthogonal. I already check that it is orthogonal. DO NOT ANSWER THIS PART. (b) Find a vector v such that d x v = m. In other words, find an affine point on the line with Plucker coordinates (1, 2, -2, -8, 5, 1). 2. Describe a general way ...continues

Estimating errors in measuring volume of small balls in large container

Consider an experimental procedure to measure the average volume of M&M Peanut candies. One hundred piece of the candy are poured into a graduated cylinder with a 30 diameter. The cylinder is then filled with 1 mm diameter beads and shaken so that the beads and candies pack as tightly as possible. Finally, the candies are remove ...continues

High School Geometry and Algebra review questions

(See attached file for full problem description)

Refer to circle A at right, which has radius 12.

Refer to circle A at right, which has radius 12. 1. Find the circumference Full problem in attached file.

Order and neighbors

For an integer n, define the graph Tn as follows: Vertices are 2-element subsets of {1,2,...,n}. Two vertices are adjacent if they have one element in common. (a) What are the order and the size of this graph? (b) How many neighbors does each vertex have? (c) Draw T5.