[/quote]
,
to 
(including 
(product) between each number. Then he writes the rest of the numbers in the denominator and also writes 
prime number, there exists only one positive number 
that makes the equation 
a perfect square of a positive integer
,
is a power of 
.
where 
is a positive integer.
determine the minimum and maximum value of![\[\frac{\sum_{i,j=1}^n|a_i+a_j|}{\sum_{i=1}^n|a_i|}.\]](http://latex.artofproblemsolving.com/6/f/2/6f2427edf9a5e8e8f2e12276d0a841765e8322f1.png)
and 
of a circle intersect at 
,
.
and 
are the intersections of the segments 
and 
and 
.
such that 
is a perfect square.
.
and 
lie on segments 
,
and 
intersect at point 
.
and 
intersect at a second point 
.
intersect at a second point 
.
lies on segment 
such that 
.
and 
are similar.
the set of all positive real numbers.
which have the property:![\[f(x)f(y)=2f(x+yf(x))\]](http://latex.artofproblemsolving.com/4/f/f/4ffbde35ff082585a188c1a4368d39338d1b07a4.png)
and 
.
such that :
for which there exists a sequence 
of positive integers satisfying the following conditions:[list]
for all integers 
for all integers 
the sequence 
is a permutation of
[/list]
is a positive integer.
be positive real numbers such that 
.
.
q
answer choices. A participant who answers all questions correctly will receive a gift. To ensure that at least one member of my family answers all questions correctly, how many family members need to take the quiz?
,
Y by
Dear Mathlinkers,
1. ABCD a square
2. (A) the circle with center at A passing through B
3. P the points of intersection of the segment AC and (A)
4. I the midpoint of AB
5. Q the point of intersection of the segment IC and (A)
6. M the foot of the perpendicular to (AB) through P.
7. Y the point of intersection of the segment MC and (A)
8. X the point of intersection de AY and BC.
Prove : QX is parallel to AB.
Jean-Louis
1. ABCD a square
2. (A) the circle with center at A passing through B
3. P the points of intersection of the segment AC and (A)
4. I the midpoint of AB
5. Q the point of intersection of the segment IC and (A)
6. M the foot of the perpendicular to (AB) through P.
7. Y the point of intersection of the segment MC and (A)
8. X the point of intersection de AY and BC.
Prove : QX is parallel to AB.
Jean-Louis
This post has been edited 2 times. Last edited by jayme, Apr 28, 2025, 1:29 PM
Reason: typo
Reason: typo
