Question

Follow the following steps of constructions:

1) Draw a line segment OA.

2) With O as center and a short radius, draw an arc that cuts OA at B.

3) With B as center and the same radius (as in step 2), draw an arc that cuts the first arc at C.

4) With C as center and the same radius (as in step 2), draw an arc that cuts the first arc at D.

5) With C and D as centers, draw two arcs with equal radii such that they intersect at E.

6) Join O and E. What’s the measure of $\angle AOE$ ?

• A. ${60}^{\circ }$
• B. ${45}^{\circ }$
• C. ${75}^{\circ }$
• D. ${90}^{\circ }$

Answer 1

The correct option is D

${90}^{\circ }$

1) Draw a line segment OA.

2) With O as center and a short radius, draw an arc that cuts OA at B.

3) With B as center and the same radius (as in step 2), draw an arc that cuts the first arc at C.

4) With C as center and the same radius (as in step 2), draw an arc that cuts the first arc at D.

5) With C and D as centers, draw two arcs with equal radii such that they intersect at E.

6) Join O and E.

The steps given above are the steps to construct ${90}^{\circ }$. So, $\angle AOE={90}^{\circ }$