Question

Draw an arc with seg AB = 6.3 cm inscribing $\angle$ACB=65$°$.

Answer 1

Chord AB subtends an $\angle$ACB.
$\angle$AOB is inscribed in arc ACB.
$\angle$AOB is the centre angle.

$$\begin{gathered} \angle \mathrm{ACB}=65° \\ \angle \mathrm{AOB}=130° \\ \therefore \angle \mathrm{OAB}=\angle \mathrm{OBA}=25° \end{gathered}$$

Steps of construction:
1. Draw a segment AB= 6.3 cm.
2. Draw rays AX and BY making an angle of $25°$ on the same side. O is the intersection point of these rays.
3. Draw an arc with centre O and radius OA or OB on the centre side.
4. Take a point C on the arc. Join CA and CB.
Thus, arc ACM is the required arc.