Mathematics
Using ruler and compasses only, construct a ΔABC such that AB = 4.6 cm, BC = 3 cm and ∠ABC = 30°. Complete the rhombus ABDE such that C is equidistant from AB and BD. Locate the point Q on BC such that Q is equidistant from A and B.
Answer
Steps of construction:
Draw a line segment AB = 4.6 cm.
Draw BZ such that ∠ABZ = 30°.
From BZ cut off BC = 3 cm, ∠ABC = 30°.
Join AC.
Since, C is equidistant from AB and BD, thus it will lie on the angle bisector of angle between AB and BD. Since, ∠ABC = 30°.
∴ ∠ABR = 60°
Draw ∠ABR = 60°.
From BR cut off BD = 4.6 cm, ∠ABD = 60° .
With D and A as center draw arcs of 4.6 cm cutting each other at point E.
Join DE and AE. Complete the rhombus ABDE .
Draw XY, the perpendicular bisector of AB.
Mark point Q as the intersection point of BC and XY.
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