Difference between revisions of "2006 Romanian NMO Problems/Grade 9/Problem 3"

m
m
Line 10: Line 10:
 
{{solution}}
 
{{solution}}
 
==See also==
 
==See also==
*[[2006 Romanian NMO Problems/Problem 2 | Previous problem]]
+
*[[2006 Romanian NMO Problems/Grade 9/Problem 2 | Previous problem]]
*[[2006 Romanian NMO Problems/Problem 4 | Next problem]]
+
*[[2006 Romanian NMO Problems/Grade 9/Problem 4 | Next problem]]
 
*[[2006 Romanian NMO Problems]]
 
*[[2006 Romanian NMO Problems]]
 
[[Category: Olympiad Geometry Problems]]
 
[[Category: Olympiad Geometry Problems]]

Revision as of 00:11, 11 November 2006

Problem

We have a quadrilateral $ABCD$ inscribed in a circle of radius $r$, for which there is a point $P$ on $CD$ such that $CB=BP=PA=AB$.

(a) Prove that there are points $A,B,C,D,P$ which fulfill the above conditions.

(b) Prove that $PD=r$.

Virgil Nicula

Solution

This problem needs a solution. If you have a solution for it, please help us out by adding it.

See also