Question
Using ruler and compass construct a cyclic quadrilateral ABCD in which AC = 4 cm, ∠ ABC = 60°, AB 1.5 cm and AD = 2 cm. Also, write the steps of construction.
✓
Answer
Steps of construction:
1) Draw a line segment AC = 4 cm.
2) Draw ∠ CAX = 60°.
3) Draw the perpendicular bisector MN of AC.
4) Draw EA ⊥ AX at point A which intersects MN at O.
5) With Centre O and radius OA draw a circle.
6) Mark a point B on the circumference of the circle such that AB = 1.5 cm and mark a point D on the circumference so that AD = 2.0 cm.
7) Join BC and measure ∠ ABC = 60°. Then ABCD is the required cyclic quadrilateral.
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