Question

Draw an arc such that chord ST = 5.6 cm inscribing $\angle$SVT= 80$°$.

Answer 1

Chord ST subtends $\angle$SVT.
$\angle$SON is inscribed in arc SVT.
$\angle$SOT is the centre angle.
$$\begin{gathered} \angle \mathrm{SVT}=80° \\ \angle \mathrm{SOT}=160° \\ \therefore \angle \mathrm{TSO}=\angle \mathrm{STO}=10° \end{gathered}$$

Steps of construction:
1. Draw a segment ST = 5.6 cm.
2. Draw rays SX and TY making an angle of 10$°$ on the same side. O is the intersection point of these rays.
3. Draw an arc with centre O and radius OS or OT on the centre side.
4. Take a point V on the arc. Join SV and TV.
Thus, arc SVT is the required arc.