Question

Construct $∆$XYZ such that XY = 6.7 cm ,YZ = 5.8 cm, XZ = 6.9 cm and constructs its incircle.

Answer 1

Steps of construction:
1. Draw XZ = 6.9 cm
2. With X as centre and 6.7 cm as radius, draw an arc above the line XZ. Also, with Z as centre and 5.8 cm as radius, draw an arc cutting the previous drawn arc at point Y.
$∆$XYZ is thus obtained.
3. Construct the angle bisectors of $\angle$X and $\angle$Z and let them meet at point O.
4. Through point O, draw a perpendicular to line XZ. Let the perpendicular meet the line XZ at point P.
5. With O as centre and OP as radius, draw a circle inside the $∆$XYZ.
This is the required incircle.