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.

Steps of construction:

1. Draw a line segment AB = 4.6 cm.

2. Draw BZ such that ∠ABZ = 30°.

3. From BZ cut off BC = 3 cm, ∠ABC = 30°.

4. 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°

6. Draw ∠ABR = 60°.

7. From BR cut off BD = 4.6 cm, ∠ABD = 60° .

8. With D and A as center draw arcs of 4.6 cm cutting each other at point E.

9. Join DE and AE. Complete the rhombus ABDE .

10. Draw XY, the perpendicular bisector of AB.

11. Mark point Q as the intersection point of BC and XY.