AP is any straight line through A which meets the side BC of triangle ABC at P.O is the mid-point of AP. Prove that triangle BOC = `1/2` triangle ABC.

If the angles of a triangle ABC are in A.P. then

If the angles of a triangle ABC are in A.P. , then

P and Q are respectively the mid-points of sides AB and BC of a triangle ABC and R is the mid-point of AP, show that ar( Delta PRQ) = 1/2 ar( Delta ARC)

BM and CN are perpendiculars to a line passing through the vertex A of a triangle ABC. If Lis the mid-point of BC, prove that LM = LN.

If D is the mid-point of the side BC of triangle ABC and AD is perpendicular to AC, then

P and Q are respectively the midpoints of sides AB and BC or a triangle ABC and R is the mid-point of AP, show ar(RQC) = 3/8 ar(ABC).

P and Q are respectively the midpoints of sides AB and BC or a triangle ABC and R is the mid-point of AP, show ar(PRQ)= 1/2 ar(ARC).

If D,E,F are mid-points of the sides of triangle ABC , prove (by vectors) that area of triangle DEF= 1/4 area of triangle ABC .

P and Q are respectively the midpoints of sides AB and BC or a triangle ABC and R is the mid-point of AP, show ar(PBQ)=ar(ARC).