Question

Use ruler and compass for the following construction:

1. Construct an equilateral triangle ABC of side 5 cm.
2. Construct the circumcircle of ΔABC.
3. Construct the locus of points which are equidistant from AB and BC. Mark the point where the circumcircle and locus meet, as D.
4. Give the geometrical name of quadrilateral ABCD.

Answer 1

Steps of construction:

1. Draw a line segment AB = 5 cm.
2. At point A with radius = 5 cm draw an arc.
3. At point B with radius = 5 cm draw another arc, cutting previous arc at point C.
4. Join AC and BC.
5. Construct perpendicular bisectors of AB and BC, let the bisectors meet at point O.
6. With O as centre and OA as radius draw a circumcircle.
7. Construct angle bisector of ∠ABC, mark the point as D where angle bisector intersects circumcircle.
8. Join AD and CD.

Since points A, B, C and D lie on the circumcircle, ABCD is a cyclic quadrilateral.

Hence, ABCD is a cyclic quadrilateral.