# If D, E, F are the feet of perpendiculars from the vertices A, B, C to the opposite sides of ΔABC and the semi-perimeter of ΔDEF

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If D, E, F are the feet of perpendiculars from the vertices A, B, C to the opposite sides of ΔABC and the semi-perimeter of ΔDEF is equal to the in-radius of DABC then cosA/2cosB/2cosC/2  is equal to

(a)  1/4

(b) 1/2

(C) 1/8

(D)  3/8

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Correct option  (A)  1/4

R[sin2A + sin2B + sin2C] = 2r

⇒ 4R sinA sinB sinC = 8R sinA/2sinB/2sinC/2

⇒ cosA/2cosB/2cosC/2 = 1/4