Question

Two arcs in the circle make the equal angle at the center of the circle. then the two triangles made by the corresponding chord and the radii joint to the end points of arc are

• A. Congruent
• B. Similar

Answer 1

Answer: (A), (B)

Similar

Here, arcs $AB$ and $CD$ make equal angles at the center of the circle. and triangles so formed are $△AOB$ and $△COD$.

Now, in $△AOB$ and $△COD$
$AO=CO$ (radius of same circle)
$BO=DO$ (radius of the same circle)
$\angle AOB=\angle COD$(arcs make equal angle at center)
So, $△AOB\cong △COD$ (SAS)

Hence both triangles are congruent. And we know all congruent triangles are similar also.

So, triangles so formed will be congruent as well as similar.