Constructing and proof involving line segment

I need help with doing this problem, Given a line segment QR=1 1. Given segments qand r, constuct a line segment qr. 2. Given segments q,r,s construct a line segment qrs. I'm confused on how to set it up and begin. I have the one for constructing a line segment of length q/r. Thanks

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'.