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Geometry problems (11..20) |
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problems 1..10 |
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problems 21..29 |
11.
![](../geo16/fig1.jpg)
Calculate angle x.
![](pictures/solution.jpg)
12.
In the figure below we notice right-angled triangles and their inscribed circles.
![](../geo17/fig1.jpg)
Question: what is the area of the rectangle for these inscribed circle diameters?
![](pictures/solution.jpg)
13.
In the figure below we notice right-angled triangles and their inscribed circles.
![](../geo18/fig1.jpg)
Question: what is the area of the rectangle for these inscribed circle diameters?
![](pictures/solution.jpg)
14.
![](../geo19/fig1.jpg)
find angles x, y at point D in above picture.
![](pictures/solution.jpg)
15.
Calculate x in next picture.
![](../geo21/fig1.jpg)
![](pictures/solution.jpg)
16.
Below is pictured rectangle ABCD with BD perpendicular to CE.
Prove that BE x BA = (BC)2.
![](../geo22/fig1.jpg)
![](pictures/solution.jpg)
17.
In picture below AD = DC
LABC = 45 deg.
Question: find angle x.
![](../geo23/fig1.jpg)
![](pictures/solution.jpg)
18.
Calculate angle x.
![](../geo24/fig1.jpg)
![](pictures/solution.jpg)
19.
![](../geo26/fig1.jpg)
Triangle ABC is isosceles and right angled.
Proof that angle x = LDCE = 45 degrees.
![](pictures/solution.jpg)
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.
![](../geo27/fig1.jpg)
![](pictures/solution.jpg)
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