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Question

A line PQ is drawn and with P as centre, a circle is drawn with radius greater than half of PQ but less than PQ. Again with same radius and Q as centre, draw another circle. If the two circles meet at X and Y, then what can be said about the points X and Y?


A

They will not be on the same line

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B

The midpoint of XY lies on PQ and they coincide

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C

The midpoint of XY lies on PQ and closer to P

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D

The midpoint of XY lies on PQ and closer to Q

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Solution

The correct option is B

The midpoint of XY lies on PQ and they coincide


The above description gives the perpendicular bisector of PQ.

Alternate solution:
The quadrilateral formed by joining PXQY is a rhombus. In rhombus the diagonals are perpendicular bisectors.

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Constrcution of a perpendicular to a line from an external point.
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