\( \mathrm{G} \) is the centroid of triangle \( \mathrm{ABC} \). Pe...

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\( \mathrm{G} \) is the centroid of triangle \( \mathrm{ABC} \). Perpendiculars from vertices A, B, C meet the sides \( \mathrm{BC}, \mathrm{CA}, \mathrm{AB} \) at D, E, F respectively. P,
\( \mathrm{P} \) Q, R are feet of the perpendiculars from \( \mathrm{G} \) on sides \( \mathrm{BC}, \mathrm{CA} \),

W \( \mathrm{AB} \) respectively. L, M, \( \mathrm{N} \) are the mid points of sides \( \mathrm{BC}, \mathrm{CA} \), \( \mathrm{AB} \) respectively, then
Length of the side \( \mathrm{PG} \) is
(a) \( \frac{1}{2} \mathrm{~b} \sin \mathrm{C} \)
(b) \( \frac{1}{2} c \sin C \)
(c) \( \frac{2}{3} \mathrm{~b} \sin \mathrm{C} \)
(d) \( \frac{1}{3} \mathrm{c} \sin \mathrm{B} \)
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