A problem by Apoorva Pasbola

Level pending

D is the mid point of side BC of a triangle ABC.AD is bisected at the point E and BE produced cuts AC at the point X. The ratio of BE:EX can be expressed in the form a/b where a and b are co-prime numbers.Find a+b.


The answer is 4.

Apoorva Pasbola by Apoorva Pasbola , 24, India

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2 solutions

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Tong Zou
Dec 16, 2013

Extend A D AD to intersect with the line through B and parallel to A C AC . Call the point of intersection F. Then triangle A D C ADC is congruent to triangle F D B FDB . So D F = A D DF=AD . Also, triangle A D X ADX is similar to triangle F E B FEB . Therefore B E : E X = E F : A E = 3 : 1 BE:EX=EF:AE=3:1 .

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