Question

Abc is right triangle at c if p is the length of perpendicular c to ab and a b c are the lengths of the sides opposite angle a angle b angle c respectively then prove that 1/p2=1/a2 + 1/b2

Answer 1

-------- From proof (1)
= (1/a
+ b
= a
+ b
2
/ a
+ 1/a
/ a
(i) Area of ΔABC = 1/2 × Base × Height = 1/2 × BC × AC = 1/2 ab
    Area of ΔABC = 1/2 × Base × Height = 1/2 × AB × CD = 1/2 cp
    ⇒ 1/2 ab = 1/2 cp
    ⇒ ab = cp
    Hence proved.
(ii) In right angled triangle ABC,
+ AC
2
AB
= BC
Hence proved.
2
1