intersect at point 
.
and 
with their common external tangents lie on a circle 
.
and 
with their common external tangents lie on a circle 
.
board and made 
moves so that it visited all squares and returned to the starting square. At every moment, the distance from the center of the square the king was on to the center of the board was calculated. A move is called 
if this distance becomes smaller after the move. Find the maximum possible number of pleasant moves. (The chess king moves to a square adjacent either by side or by corner.)
grid, taking turns. Petya goes first. On his turn, a player writes an uppercase Russian letter in an empty cell (each cell can contain only one letter). When all cells are filled, Petya is declared the winner if there are four consecutive cells horizontally spelling the word ``ПЕТЯ'' (PETYA) from left to right, or four consecutive cells vertically spelling ``ПЕТЯ'' from top to bottom. Can Petya guarantee a win regardless of Vasya's moves?
Y by Mango247
A point 
is marked on the diagonal 
of parallelogram 
, which does not lie on the diagonal 
. On the ray 
, a point 
is taken such that 
. A straight line drawn through point , parallel to side 
, it crossed the side 
at point 
. Then, through point , a straight line drawn parallel to side 
, crossed line 
at point 
. Find the angle 
is marked on the diagonal 
of parallelogram 
, which does not lie on the diagonal 
. On the ray 
, a point 
is taken such that 
. A straight line drawn through point , parallel to side 
, it crossed the side 
at point 
. Then, through point , a straight line drawn parallel to side 
, crossed line 
at point 
. Find the angle 
This post has been edited 2 times. Last edited by parmenides51, Feb 22, 2021, 12:36 AM
