MHB Position vector question. Tough to solve.

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The discussion revolves around solving position vector equations involving points P, Q, O, R, and M. The first hint suggests breaking down the vector from P to Q into components from P to O, O to R, and R to Q. The second hint indicates that the vector from O to M can be expressed in terms of the vector from O to P and half the vector from P to Q. Participants are encouraged to complete these vector equations to find the relationships between the points. Completing these equations will clarify the position vectors involved in the problem.
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Hints:

1. $\displaystyle \begin{align*} \vec{PQ} = \vec{PO} + \vec{OR} + \vec{RQ} \end{align*}$. Finish it.

2. $\displaystyle \begin{align*} \vec{OM} = \vec{OP} + \vec{PM} = \vec{OP} + \frac{1}{2}\vec{PQ} \end{align*}$. Finish it.
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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