Yes, this is deliberate
by math_explorer, Sep 13, 2010, 11:45 AM
I am double-posting for two reasons:
1) to keep the marathon format
2) to boost my post count and therefore my ego
The next problem is hard, I promise.
is a trapezoid in which 
. Let the external bisectors of 
and 
intersect at 
, and let the external bisectors of 
and 
intersect at 
. Prove that 
is equal to half the perimeter of . (Mexico)
Okay, the next problem, which is hideously difficult to draw without either almost-implying the result or curving a line a lot.
and 
are points on circle 
. 
is on the tangent to circle through . 
is the midpoint of 
. 
and 
intersect the circle at resp. 
and 
. If the tangents to circle through and intersect at 
and 
are collinear, prove 
. Hmm, Bulgaria.
(I suspect that inversion might kill this problem. I'm either totally wrong or in one of those silly blind spots where the next step is so obvious it can't be found.)
1) to keep the marathon format
2) to boost my post count and therefore my ego
The next problem is hard, I promise.
Quote:
is a trapezoid in which 
. Let the external bisectors of 
and 
intersect at 
, and let the external bisectors of 
and 
intersect at 
. Prove that 
is equal to half the perimeter of . (Mexico)
and 
,
to be the resp. midpoints of 
.
.
.
.
is the median of the trapezoid, 
.Okay, the next problem, which is hideously difficult to draw without either almost-implying the result or curving a line a lot.
and 
are points on circle 
. 
is on the tangent to circle through . 
is the midpoint of 
. 
and 
intersect the circle at resp. 
and 
. If the tangents to circle through and intersect at 
and 
are collinear, prove 
. Hmm, Bulgaria.(I suspect that inversion might kill this problem. I'm either totally wrong or in one of those silly blind spots where the next step is so obvious it can't be found.)
This post has been edited 1 time. Last edited by math_explorer, Sep 15, 2010, 1:45 PM
May 2020
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