Mathematics
Describe the locus of a point in rhombus ABCD, so that it is equidistant from
(i) AB and BC.
(ii) B and D.
Locus
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Answer
(i) We know that,
The locus of a point, which is equidistant from two intersecting straight lines, is a line which bisects the angle between the given lines.
In rhombus,
The diagonals bisect the interior angles.
Hence, the locus of point in a rhombus ABCD which is equidistant from AB and BC will be the diagonal BD.
(ii) We know that,
The locus of a point, which is equidistant from two points is the perpendicular bisector of the line joining those points.
In rhombus,
Diagonals bisect each other at right angles.
Hence, the locus of point in a rhombus ABCD which is equidistant from B and D is diagonal AC.
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