Question

ABC is a right triangle right-angled at C.let BC = a , CA = b , AB = c and let p be the length of perpendicular from C on AB , prove that
(1) cp=ab
(2) 1/p2 = 1/a2 + 1/b2​

Answer 1

Answer:

1. ↦ Area is 1/2 base * height . So for the same triangle area can be 1/2*b*a and can be 1/2*p*c. Hence cp = ab

2. ↦ From above p2 = a2b2/c2

1/p2 = c2/ a2b2

but for right triangle c2 = a2 +b2

Hence 1/p2 = (a2+b2)/ a2b2

Hence 1/p2 = 1/a2+1/b2