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جواب صحیح کدام گزینه است 

The given question seems to involve a right-angled triangle \( ABC \), where \( A \hat B C = 90^\circ \). The triangle includes the medians \( AM \) and \( BN \), with \( M \) and \( N \) being the midpoints of sides \( BC \) and \( AC \), respectively. The goal is to determine the ratio of the length of \( BN \) to \( AM \), with the given value of \( AB = 2\sqrt{3} \).

Let me interpret and solve the problem:

1. **Understanding the given triangle**: 
   Since \( A \hat B C = 90^\circ \), triangle \( ABC \) is a right triangle. We know:
   - \(

در مثلث قائم‌الزاویه ABC مطابق شکل زیر، میان‌خط‌های AM و BN بر هم عمودند. اگر AB = 2√3 باشد، اندازه‌ی میان‌خط BN چند برابر AM است؟

In this problem, you will learn how to calculate the ratio of the medians in a right-angled triangle where AB = 2√3 and the medians AM and BN are perpendicular to each other. The solution involves using properties of medians and basic geometric principles. Suitable for students in Grades 10-12.

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