Question

Construct ΔDEF such that DE = EF = 6 cm, ∠F = 45° and constructs its circumcircle.

Answer 1

Rough figure:

DE = EF

∴ ∠DFE = ∠EDF = 45°

∴ ∠DFE = 90°

Steps of construction:

1. Construct ∆DEF of the given measurement.
2. Draw the perpendicular bisectors of side DE and side EF of the triangle.
3. Name the point of intersection of perpendicular bisectors as C.
4. Join seg CE.
5. Draw circle with centre C and radius CE.