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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.

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.

Grade:11

1 Answers

Vijay Luxmi Askiitiansexpert
357 Points
14 years ago

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

 
                Hence, traingle ABC is equilateral
 

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


 

 

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