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Manisha Mishra Grade: 11
        
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.
7 years ago

Answers : (1)

Vijay Luxmi Askiitiansexpert
357 Points
										















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.)





 

 

7 years ago
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