Question

If Priya followed these instructions, what information is guaranteed to betrue about her construction? (Hint: you may want to follow themyourself.)

Answer 1

The quadilateral can be formed as,

As both the circle have same radius AB, hence the radius of the circle with center A have,

AC=AB=AD.....(1)

Also for circle with center B,

BD=BA=BC....(2)

From (1) and (2),

AB=BC=CD=DA.

Thus,all four sides of the quadilateral are equal.

But triangle ABC is an eqilateral triangle from equation (1) and (2), hence angle C will be 60 degrees.

A quadilateral with all four sides equal and one angle equals to 60 degrees must be rhombus.

Thus, option (a) is correct.