Question

AB - ACC
29 In a ∆ABC, D & E are the
points of trisection of
the side BC. Then the value of
AB^2-AC^2÷AD^2-AE^2 is
​

Answer 1

Answer:

ANSWER

Let AB,BC,AC be 3x,3y,3z

So, DF,BD,EC be x,y,z

A(ΔABC)

A(ΔEDC)

=

2

1

×AC×BCsinC

2

1

×EC×CDsinC

A(ΔABC)

A(ΔEDC)

=

2

1

×3z×3ysinC

2

1

×z×2ysinC

A(ΔABC)

A(ΔEDC)

=

9

2

Hence, option A is correct.

A(ΔBFD)

A(ΔABC)

=

2

1

×BF×BDsinB

2

1

×AB×BCsinB

A(ΔBFD)

A(ΔABC)

=

2

1

×x×ysinB

2

1

×3x×3ysinB

A(ΔBFD)

A(ΔABC)

=

1

9

A(ΔBFD)

A(ΔABC)

−1=

1

9

−1

A(ΔBFD)

A(AFDC)

=

1

8

A(ΔBFD)=

8

1

×A(AFDC)

Hence, option B is also correct.

Same can be proved for option C as in A.

A(ΔEDC)+A(ΔDBF)+A(ΔAFE)=2A(ΔDEF)

A(ΔABC)−A(ΔDEF)=2A(ΔDEF)

A(ΔABC)=3A(ΔDEF) which is incorrect since A(ΔABC)=

2

9

A(ΔDEF)