

Geometry problems (1..10) 




problems 11..20 
1.
Given are:
 a circle with radius r_{1} and inside
 two circles with radius r_{2} and r_{3} which contact circle 1 at points A and B
 the centers of circles 1,2 and 3.
 the intersection point P of circles 2 and 3
Prove that:
If P is on line AB then r_{1} = r_{2} + r_{3} must be true
2.
In the figure above the circles have centers M, N.
Proof, that the marked areas are equal.
3.
Given are:
Equilateral triangle ABC.
M is the center of BC and also center of a circle arc through B and C.
Arcs CF, FG and GB are equal in length.
Prove that :
CD = DE = EB.
4.
Given is a square and a line CD = AB.
Some angles (indicated by a small red square) are 30^{0}
Asked is the sum of angles a+b.
5.
Given are points A and B and a circle c.
Construct a circle through A and B that intersects c in diametrically opposite points.
6.
Given is square ABCD.
Triangle CDP is equilateral.
Calculate the size of LBAP.
7.
Given are:
1. ΔABC with point D on BC such that AB=DC.
2. The relative size of some angles, see figure (in blue).
Asked: find the value of x.
8.
Problem: calculate angle x in figure below:
9.
AD=DB
Question: prove that x=22.5
10.

