Mathematics
Using ruler and compasses only, construct a rhombus ABCD whose diagonals AC and BD are 8 cm and 6 cm long respectively. Find by construction a point P equidistant from AB and AD and also equidistant from C and D. Measure PC.
Locus
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Answer
Steps of construction :
Draw AC = 8 cm and BD = 6 cm as diagonals perpendicular and bisecting each other. Join the points to form rhombus ABCD.
Since, diagonals of rhombus bisects vertices, hence, AC is angular bisector of BAD.
Draw RS, the perpendicular bisector of CD.
The intersection of RS and AC is the point P which satisfies both i.e. it is equidistant from AD, AB and C and D also.
On measuring we get, CP = 3.1 cm.
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