Thread: Question on triangles?

D, E and F are the middle points of the sides of triangle ABC then the correct statement(s) is/are:

A) centroid of the triangle DEF coincides with the centroid of the triangle ABC

B)orthocentre of the triangle DEF is the circumcentre of the triangle ABC

C) area of triangle DEF = 4 * (area of triangle DEF)

D) None of these

C is correct for sure. Which other options are correct?

Originally Posted by fardeen_gen

D, E and F are the middle points of the sides of triangle ABC then the correct statement(s) is/are:

A) centroid of the triangle DEF coincides with the centroid of the triangle ABC

B)orthocentre of the triangle DEF is the circumcentre of the triangle ABC

C) area of triangle DEF = 4. area of triangle DEF

D) None of these

C is correct for sure. Which other options are correct?

A) is wrong, draw a picture to prove so
C) This doesn't even make sense, did you mean area of triangle ABC = 4*Area(Triangle DEF)? If so, then note that the legs of DEF are half the size of the legs of ABC, the area of ABC is equal to 0.5bh, but now the base and height go down 50%, so the area of DEF is equal to 0.5^3 bh which is 25% the size of the larger triangle, so this statement is TRUE

If C is true and this is a single choice question, then C is your answer.

What about B?Its not a single choice question.

Originally Posted by fardeen_gen

What about B?Its not a single choice question.

I cannot answer on ortho and circum-centres without looking such terms up...

Okay, it seems that the orthocentre is the point of intersection, of the perpendicular lines from the vertices to the opposite leg, of the triangle. Both of these triangles are equilateral, but do not have the same orthocentres. By drawing this out, it seems that the circumcentre, intersection of three perpendicular bisectors, of the larger triangle is the same point as the orthocentre of the smaller inscribed triangle.