Question

Construct the incircle of $∆$STU in which ST = 7 cm, $\angle$T= 120$°$ and TU = 5 cm.

Answer 1

Steps of construction:
1. Draw a line segment ST= 7 cm.
2. Draw $\angle \mathrm{STX}=120°$.
3. With T as the centre and a radius of 5 cm, draw an arc cutting TX at U.
4. Join SU.
5. Then $∆$STU is the required triangle.
6. Draw angle bisectors of $\angle \mathrm{STU}\mathrm{and}\angle \mathrm{TSU}$ (any two angles) which intersect at I.
7. From point I, draw a perpendicular IL on side SU.
8. Taking IL as the radius, draw the required in circle.