Circumscribable quadrilateral and finding lengths

In the attached figure, the quadrilateral ABCD has the following lengths of sides and diagonals: DC=7, CB=8, BA=13, AD=13, AC=15, and BD=13. 1. Verify that quadrilateral ABCD is circumscribable 2. Find the remaining lengths of DE, BE, AE, and CE. Although it appears there is a right angle, it is not labeled as though it is, so treat it like there is not a right angle.

Construct a geometric model using axioms

Construct a model that satisfies the following axioms. - 1. There exists at least 1 line. - 2. Every line of the geometry has exactly 4 points on it. - 3. Not all points of the geometry are on the same line. - 4. Each point of the geometry is contained in exactly 3 lines. - 5. Every pair of lines intersect and their intersection is exactly 1 point.

Poincare half plane and h-line

Given points A(2,5) and B(6,3) in the Poincare half plane where the axis is the line that determines the half plane - A. Find the equation of the h-line that passes through A and B - B. Find AB* using the definition of distance shown in the attachment: AB* = absolute value (ln(AM x BN)/(BM x AN))) - C. Find 2 points C and D (distinct from B) such that AC*=AD*=AB*

Geometric constructions

USING ONLY AN UNMARKED STRAIGHT EDGE AND A COMPASS CONSTRUCT THE FOLLOWING: (A) A RHOMBUS GIVEN: ONE SIDE AND ONE ANGLE (B) A PARALLELOGRAM GIVEN: TWO ADJACENT SIDES AND THE INCLUDED ANGLE (C) A PARALELLOGRAM GIVEN: THE DIAGONALS AND THE ANGLE BETWEEN THEM ********I NEED STEP-BY-STEP INSTRUCTIONS ON HOW TO CONSTRUCT EACH OF THESE - YOU CAN USE DRAWINGS IF THAT IS EASIER. I HAVE TO BE ABLE TO CONSTRUCT THESE ON MY OWN AND I HAVE NEVER DONE CONSTRUCTIONS BEFORE THIS ASSIGNMENT!!!!!!! SO PLEASE, PLEASE, PLEASE BE SPECIFIC!

Centriod-Balance Point Proog

Need to prove that centroid of a triangular region is the balance point. Trick is that I can't use the "equal areas" argument.