Geometry puzzle solutions 9 (80..89)
80.
In figure below AB=AC=AD
Calculate angle x.



Solution



81.
Three equal circles lay tight within rectangular triangle ABC.
Calculate radius r of the circles.



Solution




Using trigonometry a faster solution is possibel:



Proof:


82.
In a square circles with radius R and r are tight between quarter circles.
(center of circles on corners).
Calculate ratio R/r.



Solution



83.
Prove that the area of triangle ABC [ABC] = pq



Solution



84.
Calculate angle x.



Solution



85.
Two lines separate square ABCD in three equal areas.
The distance between the lines is 1.
Calculate the area of the square.



Solution



86.
Below is pictured a regular hexagon and a random point inside.
Calculate area x.



Solution


87.
Calculate the shaded area A.



Solution


88.
Calculate the shaded area.



Solution


89.
Calculate the ratio of green/orange square areas.



Solution