Question

triangle ABC is right angled at C. if P is the length of perpendicular from C to AB and a, b, c are the length of the sides opposite angle A, angle B angle C respectively. then prove that 1/psquare = 1/ asquare + 1/bsquare


can anyone please solve this as soon as possible ​

Answer 1

Answer:

c^2 = a^2 +b^2 eq 1

area of triangle =(1/2)a.b=(1/2)p.c

ab=pc

p^2.c^2 = a^2.b^2. eq 2

divide eq 1 by eq 2

c^2/(p^2.c^2) = (a^2 + b^2)/(a^2.b^2)

1/p^2 = 1/b^2 + 1/a^2 proved