Lex X by any point on the side BC of a triangle ABC. If XM, XN are drawn parallel to BA and CA meeting CA, BA in M, N respectively; MN meets BC produced in T, prove that `T X^2=T B x T Cdot`

Let X be any point on side BC of DeltaABC, XM and XN are drawn parallel to BA and CA. MN meets in T. Prove that TX^(2)=TB.TC.

ABC is a triangle A line is drawn parallel to BC to meet AB and AC in D and E respectively. Prove that the median through A bisects DE.

ABC is a triangle A line is drawn parallel to BC to meet AB and AC in D and E respectively. Prove that the median through A bisects DE.

Given triangle ABC, lines are drawn through A, B and C parallel respectively to the sides BC, CA and AB forming PQ . Show that BC= 1/2 QR

The side BC of a triangle ABC is bisected at D; O is any point in AD. BO and CO produced meet AC and AB in E and F respectively and AD is produced to X so that D is the mid-point of OX. Prove that AO:AX=AF:AB and show that FE||BC.

The side BC of a triangle ABC is bisected at D;o is any point in AD,BO and CO produced meet AC and AB in E and F respectively and AD is produced to X so that D is the mid-point of OX. Prove that AO:AX=AF:AB and show that FE|BC.

The side B C of a triangle A B C is bisected at D ; O is any point in A D. BO and CO produced meet AC and AB in E and F respectively and A D is produced to X so that D is the mid-point of O X . Prove that A O : A X=A F : A B and show that FE||BC .

The diameters of the circumcirle of triangle ABC drawn from A,B and C meet BC, CA and AB, respectively, in L,M and N. Prove that (1)/(AL) + (1)/(BM) + (1)/(CN) = (2)/(R)

The diameters of the circumcirle of triangle ABC drawn from A,B and C meet BC, CA and AB, respectively, in L,M and N. Prove that (1)/(AL) + (1)/(BM) + (1)/(CN) = (2)/(R)