# A geometry problem by Pankhuri Agarwal

Geometry Level pending

Consider a circle in the $$XY$$ plane with diameter $$1$$, passing through the origin $$O$$ and through a point $$A=(1,0)$$. For any point $$B$$ on the circle, let $$C$$ be the point of intersection of the line $$OB$$ with the vertical line through $$A$$. If $$M$$ is the point on the line $$OBC$$ such that $$OM$$ and $$BC$$ are of equal length, then the locus of point $$M$$ as $$B$$ varies is given by the equation $$\text{__________}$$.

×