Question

Construct a segment of a circle given an angle of ${90}^{\circ }$ and chord 5 cm.

Answer 1

Steps of constructions:

Rough image:

Explanation:

$x+x+{90}^{\circ }={180}^{\circ }$

[using sum of all angles in a triangle $={180}^{\circ }$]

$\Rightarrow 2x+{90}^{\circ }={180}^{\circ }$

$\Rightarrow 2x={180}^{\circ }-{90}^{\circ }$

$\Rightarrow 2x={90}^{\circ }$

$\Rightarrow x=\frac{{90}^{\circ }}{2}={45}^{\circ }$

Step 1: Draw a line segment AB=5cm

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

Step 3: With center "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.