Question

Use a ruler and compass only for this question to construct the cyclic quadrilateral ABCD in which AB = 5 cm, BC = 8 cm, ∠ ABC = `67 1/2 °`, and D is equidistant from B and C.

Answer 1

Steps of construction:
1) Draw BC = 8 cm, Construct ∠ B = ` 67 1/2°` and Cutoff AB = 5 cm.
2) Draw bisector of BC and AB and produce these to meet at O.
3) With O as the centre, radius OA or Ob or OC draw a circle to pass-through ∠ABC.
4) Produce the bisector of BC to interest the circumference of the circle. This intersection point is D.
5) Join CD and AD.
6) ABCD is the required cyclic quadrilateral. Length of CD = 6.4 cm.    ....(By measurement).