Triangle PQR is an equilateral triangle inscribed in a triangle ABC such that P lies on BC, Q on CA and R on AB. If BP/PC=CQ/QA=AR/RB. Prove that triangle ABC is also equilateral.

Dear Manisha,

        Below is the figure as per your question:-

        =>     BP : CQ : QR = PC : AQ : BR

        =>     BP : CQ : AR = PR : PQ : QR

                                = 1 : 1 : 1 [traingle PQR is equilateral]

        =>     AB : BC : AC = 1 : 1 : 1

(Basically this problem is given to visualization and symmetry, mentioning in cash and every point on the paper is very difficult.)