P-P Situation 4: Problem 9. and Problem 10.
P-P Situation 4:
A. Create a formula to calculate the sum of the areas of the arbeloses, which are constructed externally on the sides of the equilateral triangle, if the tangential points of the two small semicircles of each arbelos are the medium points of the triangle sides. Post GeoGebra construction.
B. Post GeoGebra construction, which is a generalisation of the problem in the condition A. Bring a new formula for calculating the sum of the areas of the arbeloses which are constructed externally on the sides of a triangle.
Problem 9.
If on the sides of any triangle are constructed arbeloses and the tangential points of two small semicircles of each arbelos are the medium points of the respective sides of the triangle, then the formula for calculating the sum of arbeloses' areas is where are the radii of the biggest semicircles and are the radii of the small semicircles of the arbeloses, respectively.
Problem 10.
If on the sides of any triangle are constructed arbeloses, then the formula for calculating the sum of their areas is where and are the radii of the biggest semicircles and and are the radii of the small semicircles of the arbeloses, respectively.