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2006 Romanian NMO Problems/Grade 9/Problem 3

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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

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