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Circles — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsCircles1 Mark
Question
Write ‘True’ or ‘False’ and justify your answer.
If a number of circles pass through the end points P and Q of a line segment PQ, then their centres lie on the perpendicular bisector of PQ.
✓

Answer

True.
Centre of any circle passing through the end points $P$ and $Q$ of a line segment are equidistant from $P$ and $Q . \therefore A_1 P=$ $A_1 Q A_2 P=A_2 Q A_3 P=A_3 Q$ as we know that any point on perpendicular bisector of a segment is equidistant from the end point of the segment. Hence, $A_1, A_2, A_3$ points are the centres of circles passing through the end points $P$ and $Q$ of a segment PQ or the centeres of circles lie on the perpendicular bisector of PQ.

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