MathDB
2013 preRMO p17, 3 circles, tangent, radius wanted

Source:

August 8, 2019
geometrycirclesradius

Problem Statement

Let SS be a circle with centre OO. A chord ABAB, not a diameter, divides SS into two regions R1R_1 and R2R_2 such that OO belongs to R2R_2. Let S1S_1 be a circle with centre in R1R_1, touching ABAB at XX and SS internally. Let S2S_2 be a circle with centre in R2R_2, touching ABAB at YY, the circle SS internally and passing through the centre of SS. The point XX lies on the diameter passing through the centre of S2S_2 and ∠YXO=30o\angle YXO=30^o. If the radius of S2S_2 is 100100 then what is the radius of S1S_1?
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