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.

Asked:
Express r in a and b.