Difference between revisions of "2006 Romanian NMO Problems/Grade 9/Problem 3"
m |
|||
| Line 1: | Line 1: | ||
==Problem== | ==Problem== | ||
| − | We have a quadrilateral <math>ABCD</math> | + | We have a [[quadrilateral]] <math>ABCD</math> [[inscribe]]d in a [[circle]] of [[radius]] <math>r</math>, for which there is a [[point]] <math>P</math> on <math>CD</math> such that <math>CB=BP=PA=AB</math>. |
(a) Prove that there are points <math>A,B,C,D,P</math> which fulfill the above conditions. | (a) Prove that there are points <math>A,B,C,D,P</math> which fulfill the above conditions. | ||
| Line 8: | Line 8: | ||
''Virgil Nicula'' | ''Virgil Nicula'' | ||
==Solution== | ==Solution== | ||
| + | {{solution}} | ||
==See also== | ==See also== | ||
| + | *[[2006 Romanian NMO Problems/Problem 2 | Previous problem]] | ||
| + | *[[2006 Romanian NMO Problems/Problem 4 | Next problem]] | ||
*[[2006 Romanian NMO Problems]] | *[[2006 Romanian NMO Problems]] | ||
[[Category: Olympiad Geometry Problems]] | [[Category: Olympiad Geometry Problems]] | ||
Revision as of 23:10, 10 November 2006
Problem
We have a quadrilateral 
inscribed in a circle of radius 
, for which there is a point 
on 
such that 
.
(a) Prove that there are points 
which fulfill the above conditions.
(b) Prove that 
.
Virgil Nicula
Solution
This problem needs a solution. If you have a solution for it, please help us out by adding it.
