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problems 50..59
problems 70..79
60.
![](../geo64/fig1.jpg)
Calculate edges AB and AC.
![](pictures/solution.jpg)
61.
Given is square ABCD.
DF=a; BE=b;AF=x;
LBAE=LEAF.
Prove that x=a+b;
![](../geo65/fig1.jpg)
![](pictures/solution.jpg)
62.
![](../geo66/fig1.jpg)
Calculate radius r of the smallest circle.
![](pictures/solution.jpg)
63.
Given is square ABCD.
AB=a; FC=FE=b;
Prove that x2=2ab;
![](../geo67/figa1.jpg)
![](pictures/solution.jpg)
64.
Given is right angled triangle ABC with two contacting inscribed circles.
AB=5; BC=4; AC=3;
Calculate radius r of the circles.
![](../geo67/figb1.jpg)
![](pictures/solution.jpg)
65.
Calculate the area of the colored triangle.
![](../geo67/figc1.jpg)
![](pictures/solution.jpg)
66.
Prove the formula for the truncated cone.
![](../geo68/fig1.jpg)
![](pictures/solution.jpg)
67.
![](../geo69/fig1.jpg)
![](pictures/solution.jpg)
68.
![](../geo69/fig3.jpg)
![](pictures/solution.jpg)
69.
![](../geo70/fig70a1.jpg)
![](pictures/solution.jpg)
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