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Prove that |RP| = |PD|

Source: VAIMO 1, German Pre-TST 2010

July 16, 2011

geometryrhombusgeometry unsolved

Problem Statement

The quadrilateral

ABCD

is a rhombus with acute angle at

A.

Points

M

and

N

are on segments

\overline{AC}

and

\overline{BC}

such that

|DM| = |MN|.

Let

P

be the intersection of

AC

and

DN

and let

R

be the intersection of

AB

and

DM.

Prove that

|RP| = |PD|.

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