Question

Construct a segment of a circle on a chord of length $5$ cm containing the following angles.
i. ${90}^o$ ii ${45}^o$ iii ${120}^o$

Answer 1

(i) ${90}^{\circ }$ :

Steps of construction :

Step 1: Draw a line segment $AB=5$ cm.

Step 2: Draw an angle of ${45}^{\circ }$ on point $A$ and $B$ to intersect at $O$.

Step 3: With centre $O$ and radius $OA$ and $OB$, draw the circle.

Step 4: Mark a point $C$ on the arc of the circle. Join $AC$ and $BC$. We get $\angle CAB={90}^{\circ }$.

Thus, $ACB$ is the required circle segment.

(ii) ${45}^{\circ }$ :

Steps of construction :

Step 1: Draw a line segment $AB=5$ cm

Step 2: Draw an angle of ${45}^{\circ }$ on point $A$ and $B$ to intersect at $O$.

Step 3: With centre $O$ and radius $OA$ and $OB$, draw the circle.

Step 4: Mark a point $C$ on the arc of the circle. Join $AC$ and $BC$. We get $\angle ACB={45}^{\circ }$.

Thus, $ACB$ is the required circle segment.

(iii) ${120}^{\circ }$

Steps of construction :

Step 1: Draw a line segment $AB=5$ cm

Step 2: Draw an angle of ${30}^{\circ }$ on point $A$ and $B$ to intersect at $O$.

Step 3: With centre $O$ and radius $OA$ and $OB$, draw the circle.

Step 4: Mark a point $C$ under the chord $AB$ and on the arc of the circle.

Step 5: Join $AC$ and $BC$. We get $\angle A0B={240}^{\circ }$.

Thus, $ACB$ is the required circle segment.