MathDB

3

Part of 2000 May Olympiad

Problems(2)

Tangent circles

Source: May Olympiad (Olimpiada de Mayo) 2000

2/27/2018
Let SS be a circle with radius 22, let S1S_1 be a circle,with radius 11 and tangent, internally to SS in BB and let S2S_2 be a circle, with radius 11 and tangent to S1S_1 in AA, but S2S_2 isn't tangent to SS. If KK is the point of intersection of the line ABAB and the circle SS, prove that KK is in the circle S2S_2.
geometry
no of digits wanted

Source: VI May Olympiad (Olimpiada de Mayo) 2000 L1 P3

9/22/2022
To write all consecutive natural numbers from 1ab1ab to ab2ab2 inclusive, 1ab11ab1 digits have been used. Determine how many more digits are needed to write the natural numbers up to aabaab inclusive. Give all chances. (aa and bb represent digits)
Digitsnumber theory