Let \( A B C \) be an acute triangle with \( B C=a, C A=b \) and \(...

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Let \( A B C \) be an acute triangle with \( B C=a, C A=b \) and \( A B=c \), where \( a \neq b \neq c \). From any point ' \( p \) ' inside \( \triangle A B C \) let \( D, E, F \) denote foot of perpendiculars from ' \( P \) ' onto the sides \( B C, C A \)
\( \mathrm{P} \) and \( A B \), respectively. Now, answer the following questions.

W
If \( \triangle D E F \) is equilateral, then ' \( P \) '
(a) coincides with incentre of \( \triangle A B C \)
(b) coincides with orthocentre of \( \triangle A B C \)
(c) lies on pedal \( \triangle \) of \( A B C \)
(d) None of the above
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