Geometry problem solutions 7 (60..69)
60.


Calculate sides AB and AC.

Solution



61.
Given is square ABCD.
DF=a; BE=b;AF=x;
LBAE=LEAF.
Prove that x=a+b;



Solution



62.


Calculate r, the radius of the small circle.

Solution



63.
Given is square ABCD.
AB=a; FC=FE=b;
Prove that x2=2ab;



Solution



64.
Given is right angled triangle ABC with two contacting inscribed circles.
AB=5; BC=4; AC=3;
Calculate the radius of the circles.



Solution.


Note: [ABC] means : area of triangle ABC.



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65.
Calculate the area of the colored triangle.



Solution.



66.
Pictured is a truncated cone.
Prove the formula for the volume.



Solution



67.


Solution



68.


Solution



69.