Geometry · Vectors · Parallelogram · Midpoints · Ratios of segments
One afternoon Ana and Olja each walked in a straight line to visit her boyfriend: Ana to Kosta's house, Olja to Laza's house. The two routes crossed at an old tree, and there the girls met. Standing under the tree they noticed all of the following.
- Laza's house is exactly halfway along the straight route from Ana's house to the church.
- Kosta's house is exactly halfway between the bank and the church.
- The bank is as far from Olja's house as the church is from Ana's house.
- The distance from the bank to the church equals the distance between the two girls' houses.
- Looking from Ana's house towards Olja, who was standing on her own balcony, the bank lies to the right.
They agreed to meet again under the same tree at 7 in the evening, on the way home. So as not to be late, Ana asked Kosta to work out how far his house is from the old tree. Kosta knows that his house and Ana's house are \(2\) km apart. What distance will Ana walk from Kosta's house to the old tree?
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Serbian Municipal Competition 2008, high school grade I, category A, problem 3. Organized by the Mathematical Society of Serbia (DMS). Source