with 
,
.
to meet the circumcircle of 
at 
,
.
would have answer 
.
,
,
be the angles of an acute triangle such that![\[
\cos^2 A + \cos^2 B + 2 \sin A \sin B \cos C = \frac{34}{25},
\]](http://latex.artofproblemsolving.com/1/e/b/1ebfc2cbfc040795d72a9c96d212cc5b57651648.png)
and![\[
\cos^2 B + \cos^2 C + 2 \sin B \sin C \cos A = \frac{34}{25}.
\]](http://latex.artofproblemsolving.com/8/d/6/8d645f0437987d790671923ff5c9eb9e1332368a.png)
Find![\[
\cos^2 C + \cos^2 A + 2 \sin C \sin A \cos B.
\]](http://latex.artofproblemsolving.com/7/4/0/7400a4109374398e5f20914c8a3668fba7cebd9b.png)
Y by
Consider a pentagonal star formed by diagonals of an arbitrary convex pentagon.
Let's circle
segments of its outer contour one by one solid and dotted lines (see figure).
Prove that the product of the lengths of solid segments is equal to the product of the lengths of the dotted segments .
Let's circle
segments of its outer contour one by one solid and dotted lines (see figure).Prove that the product of the lengths of solid segments is equal to the product of the lengths of the dotted segments .
This post has been edited 1 time. Last edited by parmenides51, Apr 18, 2021, 7:44 PM
