Question

Construct $∆$ DEF such that DE = EF = 6 cm, $\angle$F = ${45}^{°}$ and constructs its circumcircle.

Answer 1

Steps of construction:
1. Draw a line EF = 6 cm.
2. With F as centre, draw an angle of 45$°$ using the protractor.
3. With E as centre and 6 cm as radius, cut an arc on ray FX and name it as D.
4. Join DE. $∆$DEF is thus obtained.
5. Draw the perpendicular bisectors of the lines DF and EF. Let these perpendicular bisectors meet at point O.
4. With O as centre and OE as radius, construct a circle touching all the vertices of the $∆$DEF.
This circle is thus the required circumcircle.