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9.9

Part of IV Soros Olympiad 1997 - 98 (Russia)

Problems(2)

touchpoints of incircle (IV Soros Olympiad 1997-98 Correspondence 9.9)

Source:

6/1/2024
In triangle ABCABC, angle AA is equal to aa and the altitude drawn to side BCBC is equal to hh. The inscribed circle of the triangle touches the sides of the triangle at points KK, MM and PP, where PP lies on side BCBC. Find the distance from PP to KMKM.
geometryincircle
sum of digits of divisors = 33 (IV Soros Olympiad 1997-98 R3 9.9)

Source:

6/1/2024
Find an odd natural number not exceeding 10001000 if you know that the sum of the last digits of all its divisors (including 11 and the number itself) is 3333.
number theorysum of roots