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

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==See also==
 
==See also==
*[[2006 Romanian NMO Problems/Problem 2 | Previous problem]]
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*[[2006 Romanian NMO Problems/Grade 9/Problem 2 | Previous problem]]
*[[2006 Romanian NMO Problems/Problem 4 | Next problem]]
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*[[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 23:11, 10 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

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See also