
06492944
j
2016e.00657
Murty, Gurajada Suryanarayana
A note on theorem of unequal pair of lunes.
J. Indian Acad. Math. 37, No. 1, 1318 (2015).
2015
Indian Academy of Mathematics, Indore, Madhya Pradesh, India
EN
G40
G30
area
lune
mathematical modeling
The paper proves the following result: Consider a circle and a right triangle $ABC$ such that $AB$ is a diameter of the circle. Draw semicircles with diameters $AC$ and $BC$. Each of this semicircles, together with the original circle determines a lune. The sum of the areas of these lunes equals the area of the triangle $ABC$. The result is elementary and not very surprising, Nevertheless it can be a nice excercise for secondary school students and it is suitable to be worked out with GeoGebra.
Antonio M. Oller (Zaragoza)