Difference between revisions of "2004 IMO Problems/Problem 5"
Szhangmath (talk | contribs) (→Solution) |
Szhangmath (talk | contribs) (→Solution) |
||
Line 12: | Line 12: | ||
<asy> | <asy> | ||
− | size( | + | size(6cm); |
draw(circle((0,0),7.07)); | draw(circle((0,0),7.07)); | ||
draw((-3.7,-6)-- (3.7,-6)); | draw((-3.7,-6)-- (3.7,-6)); |
Revision as of 16:44, 8 February 2024
Problem
In a convex quadrilateral , the diagonal
bisects neither the angle
nor the angle
. The point
lies inside
and satisfies
Prove that is a cyclic quadrilateral if and only if
Solution
This problem needs a solution. If you have a solution for it, please help us out by adding it.
Let be the intersection of
and
, let
be the intersection of
and
,
, so
, and
.
, so
, and
.
, so
is an isosceles triangle. Since
, so
and
are isosceles triangles. So
is on the angle bisector oof
, since
is an isosceles trapezoid, so
is also on the perpendicular bisector of
. So
.
~szhangmath
See Also
2004 IMO (Problems) • Resources | ||
Preceded by Problem 4 |
1 • 2 • 3 • 4 • 5 • 6 | Followed by Problem 6 |
All IMO Problems and Solutions |