Question

1. In ABC, m Which expression correctly relates the lengths of the

sides of this triangle?

(1) ABC BC< CA
(3) AC< BC < AB
(2) ABC AC< BC
(4) BC< AC < AB

Answer 1

4 d

Explanation:

Given D is mid-point of BC and AD⊥AC

From right angle △DAC

cosC=

a/2

b

=

a

2b

...(i)

also from cosine formulae

cosC=

2ab

a

2

+b

2

−c

2

...(ii)

From (i) and (ii) we get

a

2b

=

2ab

a

2

+b

2

−c

2

⇒4b

2

=a

2

+b

2

−c

2

⇒b

2

=

3

a

2

−c

2

∴cosAcosC=

2bc

b

2

+c

2

−a

2

.

a

2b

=

ca

[(

3

a

2

−c

2

)+c

2

−a

2

]

=

3

2

(

ca

c

2

−a

2

)