Problem C. 832.

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C. 832. Given are the points A(2,1), B(3,4), C(2,11) on the cartesian plane, show that the ray OB bisects the angle AOC.

(5 points)

Deadline expired.

Sorry, the solution is published in Hungarian only.

Megoldás:

OB $\cap$ AC=P(2;8/3)

${OC\over OA}={\sqrt{4+121}\over{\sqrt{4+1}}}=5$

${PC\over PA}={25/3\over5/3}=5$

Vagyis ${OC\over OA}={PC\over PA}$ , tehát OP (vagyis OB) az ACO háromszögben az $AOC\measuredangle$ szögfelezője.

Statistics on problem C. 832.

362 students sent a solution.

5 points: 350 students.

3 points: 1 student.

2 points: 1 student.

1 point: 4 students.

0 point: 5 students.

Unfair, not evaluated: 1 solution.

Problems in Mathematics of KöMaL, December 2005

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