In a circle with radius 4 cm the diameters ac and bd are perpendicular to each other. prove that abcd is a square. find the area of abcd.

We can show ABCD is a square by showing all the angles are right angles and congruency.
Draw two diameters that are perpendicular to each other. We can prove that they are similar by stating the intercepted arc's degree measure is twice that of the angle's. Thus, the arc is 180° and the angle intercepted is 90°. We can do this for every angle of the square. We can use Pythagorean theorem to show that the sides are equal. This can be done by setting a variable "2x" = to the side length of the square. To find x, we can use Pythagorean theorem on an isoceles triangle. 

*Note: Remember 8 is the hypotenuse because 4 is the radius, 8 is the diameter.*

Now, we solve and get 

Now we know x, 2x is just two times that. Every side can be expressed in that way. Now that we know it is a square, we can find the area by finding