Question

E and f are midpoints of the sides ab and ac of traingleabc . If bf and ce meets at o . Prove that area(obc)=area(aeof)

Answer 1

$\textbf{ \huge{ Hello Mate! }}$

Given = E and F are mid points on AB and AC of triangle ABC.

To Prove = ar( tri OBC ) = ar( □ AEOF )

To contruct = Join EF

Proof = Since E and F are mid points so EF || BC.

Since triangles BEF and CFE are on same base and altitude.

ar( tri BEF ) = ar( tri CFE )

ar( tri BOE ) + ar( tri OEF ) = ar( tri COF ) + ar( tri OEF )

ar( tri BOE ) = ar( tri COF )

Since BF is a median so

ar( tri ABF ) = ar( tri CBF )

ar( □ AEOF ) + ar( tri BOE ) = ar( tri COF ) + ar( tri OBC )

ar( □ AEOF ) = ar( tri OBC )

$\textbf{ \large{ Q.E.D }}$

$\textbf{ Have great future ahead! }$