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This problem appears to be a geometry question written in Sinhala that involves a quadrilateral \( ABCD \) and some conditions on the sides and diagonals. Let me translate and break it down:

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### Translation (Overview):
- \( ABCD \) is a quadrilateral.
- \( AB = 6a \), \( BC = 8a \), and various other sides and diagonals are mentioned.
- The forces along these sides are given as \( 12P, 3P, 4P, 3P, 15P \), which likely correspond to the sides or diagonals of the quadrilateral.
- It discusses the concept of equilibrium and finding an unknown point \( G \), possibly the center of mass or some geometric point.

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Based on the structure of the problem, it seems to involve vector equilibrium or force balance in a quadrilateral. The values given suggest that you need to solve for unknown distances or use the properties of vectors to determine a geometric relationship.

Do you want a more detailed step-by-step breakdown of how to approach solving this? I can also provide clarifications on specific parts of the problem if needed.

ABCD is a quadrilateral with side lengths AB = 6a, BC = 8a. Forces along the sides are given as 12P, 3P, 4P, 3P, and 15P. The problem involves a point G and discusses equilibrium or vector balance.

Learn how to solve a vector equilibrium problem in a quadrilateral where side lengths and forces are provided. This problem covers key geometric and vector concepts, including force balance and vector addition. Suitable for students in Grades 10-12.

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