id: 06492944
dt: j
an: 2016e.00657
au: Murty, Gurajada Suryanarayana
ti: A note on theorem of unequal pair of lunes.
so: J. Indian Acad. Math. 37, No. 1, 13-18 (2015).
py: 2015
pu: Indian Academy of Mathematics, Indore, Madhya Pradesh, India
la: EN
cc: G40 G30
ut: area; lune; mathematical modeling
ci:
li:
ab: 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.
rv: Antonio M. Oller (Zaragoza)