is it possible for a circle to pass through collinear points? – Discussion Forum

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Ayushree

Asked: July 20, 2026In: Class 9 Maths

A, B and C are three collinear points. Can you find a point P such that PA = PB = PC? What can you say about the perpendicular bisectors of AB and BC? Draw and check. Can you show that for three collinear points A, B and C, the perpendicular bisector of AB and BC are parallel? Is it possible for a circle to pass through collinear points? Can you draw a line that cuts a given circle in three distinct points?

No. There is no point that is equally distant from three collinear points. The perpendicular bisectors of AB and BC are parallel and never intersect. Therefore, no circle can pass through three collinear points.