\( A B C \) is a right angled triangle in which \( \angle B=90^{\circ} \) and \( B C=a \). If \(...

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\( A B C \) is a right angled triangle in which \( \angle B=90^{\circ} \) and \( B C=a \). If \( n \) points \( L_{1}, L_{2}, \ldots, L_{n} \) on \( A B \) are such that \( A B \) is divided in \( n+1 \) equal parts and
\( L_{1} M_{1}, L_{2} M_{2}, \ldots, L_{n} M_{n} \) are line segments parallel to \( B C \) and \( M_{1}, M_{2}, \ldots, M_{n} \) are on \( A C \), the sum of the lengths of \( L_{1} M_{1}, L_{2} M_{2}, \ldots, L_{n} M_{n} \) is
(a) \( \frac{a(n+1)}{2} \)
(b) \( \frac{a(n-1)}{2} \)
(c) \( \frac{a n}{2} \)
(d) impossible to find from the given data
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