MathDB

10.6

Part of 2010 All-Russian Olympiad Regional Round

Problems(1)

poles and polars candidate

Source: Russian Regional Olympiad 2010 10.6

8/24/2024
The tangent lines to the circle ω\omega at points BB and DD intersect at point PP. The line passing through PP cuts out from circle chord ACAC. Through an arbitrary point on the segment ACAC a straight line parallel to BDBD is drawn. Prove that it divides the lengths of polygonal ABCABC and ADCADC in the same ratio.
[hide=last sentence was in Russian: ]Докажите, что она делит длины ломаных ABC и ADC в одинаковых отношениях.
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