Geometry problems (11..20)

 problems 1..10 problems 21..29

11.

Calculate angle x.

12.
In the figure below we notice right-angled triangles and their inscribed circles.

Question: what is the area of the rectangle for these inscribed circle diameters?

13.
In the figure below we notice right-angled triangles and their inscribed circles.

Question: what is the area of the rectangle for these inscribed circle diameters?

14.

find angles x, y at point D in above picture.

15.
Calculate x in next picture.

16.
Below is pictured rectangle ABCD with BD perpendicular to CE.
Prove that BE x BA = (BC)2.

17.
In picture below AD = DC
LABC = 45 deg.
Question: find angle x.

18.
Calculate angle x.

19.

Triangle ABC is isosceles and right angled.
Proof that angle x = LDCE = 45 degrees.

20.
Given are:
A 180 degree circle arc with center P and radius c.
Within two other half circles with centers M, N and radius a ,b.
c = a + b.
Within also two small circles with radius r which touch the other circles and line AB.
AB is tangent of the inner circle arcs.