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Divide a triangle (Posted on 2010-07-07) Difficulty: 3 of 5

Let P be a point on side AB of triangle ABC.

Construct a line through P that divides the 
triangle into two polygons of equal area.

See The Solution Submitted by Bractals    
Rating: 4.0000 (1 votes)

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Solution Solution Comment 1 of 1
case1: PA < PB,
D will be the point on BC such that PD
divides ABC into two polygons of equal area.

Area of PDB = Area of ABC/2

1/2 * PB * DB * sinB = 1/2 *1/2 * AB * BC

2*PB*DB=AB*BC

2*BP/BA = BC/BD

So, extend the line BA and find the point X such
that BX = 2*BP

Join XC

Draw the line parallel to XC through P, it will
intersect BC in D.

PD is the required line.

case2: PA > PB,
D will be the point on AC such that PD
divides ABC into two polygons of equal area.

same repeats

case3: PA = PB
PA is the required line.

Edited on July 7, 2010, 4:21 pm
  Posted by Praneeth on 2010-07-07 16:18:20

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