Question

Construct the incircle of $∆$RST in which RS = 6 cm, ST = 7 cm and RT = 6.5 cm.

Answer 1

Steps of construction:
1. Draw a line segment RS = 6 cm.
2. With R as the centre and a radius of 6.5 cm, draw an arc.
3. With S as the centre and a radius of 7 cm, draw another arc cutting the previously drawn arc at point T.
4. Join RT and ST.
5. Draw the angle bisectors of $\angle \mathrm{SRT}\mathrm{and}\angle \mathrm{RST}$ (any two angles) which intersect at I.
6. From point I, draw a perpendicular IF on side RS.
7. Taking IF as the radius, draw the required incircle.