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. PC=AB
2.1/p^2=1/a^2+1/b^2.
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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