[/quote]
,
is the incentre and point 
is defined such that 
and 
is the perpendicular bisector of 
and 
be the circles passing through 
and 
respectively such that 
is tangent to 
to be a point such that it lies on both the circles 
and 
are perpendicular.
be an acute triangle. Let 
be a point on side 
and 
be a point on side 
such that lines 
are parallel. Let 
be an interior point of 
.
and 
meet side 
and 
,
and 
.
and 
intersect at a point 
.
,
are collinear.
.
and 
,
as the greatest exponent 
such that 
divides 
.
and infinitely many 
such that 
.
and 
Prove that
Let 
Prove that
Let 
Prove that
Let 
Prove that
and 
.
is given. Let 
to 
lies on the arc 
.
.
be a trapezium inscribed in a circle 
with diameter 
. The circle with center 
meets 
and 
(where 
at 
.
is perpendicular to 
.
weights, each weighing 
and another 
weights with 
each. Write a algorithm that determines the ways in which a scale can be balanced with a weight 
.
![\[ x + y^2 = p^m \]](http://latex.artofproblemsolving.com/e/c/f/ecf553036f22327dd457dc06611b6bc1b0ef072c.png)
![\[ x^2 + y = p^n \]](http://latex.artofproblemsolving.com/5/b/d/5bd672934a395aabd6865ca4b50d8da75c0fe07e.png)
For 
positive integers and 
being a prime.
and 
.
Equality holds when 
or 
.
at 
intersect again at 
.
Y by
At the base of the pyramid of volume 
lies a parallelogram. Lengths of the non-base edges of this pyramid are different and different from the lengths of the edges of its base. Find the volume a triangular pyramid made up of the side faces of this pyramid.
lies a parallelogram. Lengths of the non-base edges of this pyramid are different and different from the lengths of the edges of its base. Find the volume a triangular pyramid made up of the side faces of this pyramid.This post has been edited 1 time. Last edited by parmenides51, Jul 25, 2020, 4:53 PM
