RMO Geometry DPP 2

Radical axis questions.
Facts used:
1. 3 Pairwise Radical axes of 3 circles are concurrent.
2. Common chord of 2 circles is their R.A.(radical axis)
3. Radical axis is all those points whose powers w.r.t. 2 circles are same.
Power of a point P wr.t. a circle = PT^2 if PT is a tangent or PT1 * PT2 if a line drawn from P intersects circle at T1,T2.

Question 1: Bulgarian Mathematical Olympiad 1996. Source.













Question 2: Iranian Geometry Olympiad 2021. Source.



Note that the same reasoning would work even if the ordering is AHG and not AGH.










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