Question

Construct $∆$DAT such that DA = 6.4 cm, $\angle$D = 120$°$, $\angle$A = 25$°$ and draw incircle of $∆$DAT.

Answer 1

Steps of construction:
1. Draw a line segment DA=6.4 cm.
2. Draw $\angle \mathrm{DAY}=25°$.
3. Draw another angle $\angle \mathrm{ADX}=120°$. The rays AY and DX intersect at point T.
4. Then $∆$DAT is the required triangle.
5. Draw angle bisectors of $\angle \mathrm{DAY}\mathrm{and}\angle \mathrm{ADX}$ (any two angles) which intersect at I.
6. From point I, draw perpendicular IL on side AT.
7. Taking I as the centre and IL as the radius, draw the required incircle.