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 C`

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.

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 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)

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)

In an equilateral triangle ABC, AD is drawn perpendicular to BC meeting BC in A Prove that AD^(2) = x BD^(2) Find x.

O is any point inside a triangle ABC. The bisector of /_AOB,/_BOC and /_COA meet the sides AB,BC and CA in point D, and F respectively.Show that ADxBExCF =DBxECFA

In triangle ABC, D and E are points on side AB such that AD = DE = EB. Through D and E, lines are drawn parallel to BC which meet side AC at points F and G respectively. Through F and Glines are drawn parallel to AB which meet side BC at points M and N respectively. Prove that : BM = MN = NC.