[/quote]
,
.
.
,
,
cut three common chords concurrent at 
.
,
which are internally tangent to all 
.
.
be a point on 
,
be a line passing through 
.
at 
and the circumcircle of triangle 
at 
)
and 
are tangent at 
be a distribution function. Prove that for any 
,![\[
G(x) = \frac{1}{2h} \int_{x-h}^{x+h} F(t) \, dt
\]](http://latex.artofproblemsolving.com/5/5/d/55d81a7d36b0a052ddeb3e189645e43eb41f61a5.png)
be nonnegative real numbers such that 
.
,
satisfying 
.
satisfying:
of complex numbers satisfying 
and 
.
Y by Creativename27
How many spheres are needed to shield a point source of light?
Unfortunately, I didn't find a suitable solution for it on the page below:
https://artofproblemsolving.com/community/c4h1469498p8521602
Here too, two different solutions are given:
https://math.stackexchange.com/questions/2791186
Unfortunately, I didn't find a suitable solution for it on the page below:
https://artofproblemsolving.com/community/c4h1469498p8521602
Here too, two different solutions are given:
https://math.stackexchange.com/questions/2791186
This post has been edited 3 times. Last edited by mofidy, Mar 11, 2025, 1:08 PM
spheres suffice. Indeed, let 
be the light source, 
be a regular tetrahedron inscribed in the unit sphere 
with center 
with center 
passing through a point very close to 
.
shield 
.
are coplanar, then the line through 
does not cut any sphere. Otherwise define 
and 
.
does not cut any sphere since 
makes acute and equal angles with 
.
