(Q9) 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 (i) pc = ab (ii)

1

p²

=

1

a²

+

1

b²

Solution :

(i) CD ⊥ AB and CD = p

Area of ∆ABC =

1

2

× × =

1

2

cp
also Area of ∆ABC =

1

2

× × =

1

2

ab
⇒

1

2

cp =

1

2

ab

∴ pc = ab

(ii) Since ∆ABC is a right triangle right angled at C.

AB² = ² + ²

c² = a² + b²

[

]² = a² + b²

1

( )²

=

a² + b²

a²b²

=

1

a²

+

1

b²