Question

Construct incircle of $∆$SGN such that SG = 6.7 cm, $\angle$S = 70$°$, $\angle$G = 50$°$ and draw incircle of $∆$SGN

Answer 1

Steps of construction:
1. Draw a line segment SG = 6.7 cm.
2. Draw $\angle \mathrm{SGX}=50°$.
3. Draw another angle $\angle \mathrm{GSY}=70°$.
4. The rays GX and SY intersect at point N.
5. Then $∆$SGN is the required triangle.
6. Draw angle bisectors of $\angle \mathrm{SGX}and\angle \mathrm{GSY}$ (any two angles) which intersect at O.
7. From point O, draw perpendicular OC on side SG.
8. Taking OC as the radius, draw the required incircle.