1) p1,p2,p3 arte the altitudes of a triangle ABC drawn from the vertices A,B and C respecively . If △ is the area of the triangle and 2s is the sum of its sides a,b and c , then 1p1+1p2−1p3= A) s−a△ B) s−b△ C) s−c△ D) s△ Answer: Option DExplanation:Given BC=a, AC-b AB=c, AD=P1 BE= p2 , CF= p3 In △ABC sinB=p1c⇒1p1=1csinB Similarly , 1p2=1asinC and 1p1=1bsinA ∴ 1p1+1p2−1p3=1csinB+1asinC−1bsinA =a2△+b2△−c2△=12△(a+b−c)=2(s−c)2△=(s−c)△ ∴ 1p1+1p2−1p3= s△