Question

In triangle ABC ,D and E are the midpoints of AB and AC respectively.If the perpendiculars D and E to the sides AB and Ac meet at O .Prove OA=OB=OG​

Answer 1

Answer:

Given :

D and E are the mid-points of AB and AC respectively.

∴ 2AD=AB and 2AE=AC ....... (1)

Area of a triangle =

2

1

× base × height

∴ Area of △ABC=

2

1

×AC×AB

Since ADE form a triangle,

∴ Area of △ADE=

2

1

×AE×AD

=

2

1

×

2

AC

×

2

AB

=

4

1

×

2

1

×AC×AB

=

4

1

(Area of △ABC)

Area of △ADE=

4

1

(Area of △ABC)