Question

Construct the incircle of $∆$DEF in which DE = EF= 5.8 cm, $\angle$DEF= 65$°$ .

Answer 1

Steps of construction:
1. Draw a line segment DE= 5.8 cm.
2. Draw an angle $\angle \mathrm{DEX}=65°$.
3. With E as the centre and a radius of 5.8 cm, draw an arc cutting EX at F.
4. Join DF.
5. Then $∆$DEF is the required triangle.
6. Draw angle bisectors of $\angle \mathrm{DEF}\mathrm{and}\angle \mathrm{EDF}$ (any two angles) which intersect at I.
7. From point I, draw a perpendicular IL on side DE.
8. Taking IL as the radius, draw the required in circle.