Difference between revisions of "2004 IMO Problems/Problem 5"
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label("$D$", (-5,5), W); | label("$D$", (-5,5), W); | ||
label("$P$", (0,-1.3), N); | label("$P$", (0,-1.3), N); | ||
− | label("$K$", (-1. | + | label("$K$", (-1.6,-1.5), E); |
− | label("$L$", (0.8,-1. | + | label("$L$", (0.8,-1.5) ); |
</asy> | </asy> | ||
Revision as of 16:46, 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 |