Question

Using ruler and compass only, construct a ΔABC such that BC = 5 cm and AB = 6.5 cm and ∠ABC = 120°

1. Construct a circumcircle of ΔABC
2. Construct a cyclic quadrilateral ABCD, such that D is equidistant from AB and BC.

Answer 1

1. Construct a circumcircle of ΔABC.
   • Construct ΔABC using BC = 5 cm, AB = 6.5 cm, and ∠ABC = 120°.
   • Draw the perpendicular bisectors of AB and BC.
   • Their point of intersection O is the circumcentre.
   • With centre O and radius OA (or OB or OC), draw a circle.
     This circle is the circumcircle of ΔABC.
2. Construct a cyclic quadrilateral ABCD such that D is equidistant from AB and BC.
   • Draw the angle bisector of ∠ABC.
   • Extend it to meet the circumcircle at point D.
   • Since D lies on the angle bisector, it is equidistant from AB and BC.
   • Join AD and DC to obtain a cyclic quadrilateral ABCD.