Parting 4 ways

Geometry Level 3

The following figure is a triangle A B C ABC , where A B = 5 , B E = y , E C = 4 , C F = x , A F = 6 − x AB=5, BE = y, EC=4, CF = x, AF = 6-x .

The point D D is the Incenter of this triangle. Find the value of x + y x+y .

511 3 \frac{511}{3} 4 199 30 \frac{199}{30} 766 111 \frac{766}{111} 13 2 \frac{13}{2}

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Victor Paes Plinio by Victor Paes Plinio , 21, Brazil

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2 solutions

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Deepak Kumar
Nov 6, 2015

Hint:use the fact that an internal angle bisector divides the opposite side internally in the ratio of the sides containing the angle.

1 Helpful 0 Interesting 0 Brilliant 0 Confused

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