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Found problems: 1

2025 India National Olympiad, P3
Euclid has a tool called splitter which can only do the following two types of operations : • Given three non-collinear marked points $X,Y,Z$ it can draw the line which forms the interior angle bisector of $\angle{XYZ}$. • It can mark the intersection point of two previously drawn non-parallel lines . Suppose Euclid is only given three non-collinear marked points $A,B,C$ in the plane . Prove that Euclid can use the splitter several times to draw the centre of circle passing through $A,B$ and $C$. [i]Proposed by Shankhadeep Ghosh[/i]
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