Diagonal Length

Geometry Level 1

In the figure below, O is the center of the circle with radius 2 and vertex of the square OABC. What is the length of AD?

1 2 0.5 1.414

3 solutions

A Former Brilliant Member
Jun 23, 2018

$OB$ is the radius of the circle and $OB=AD=\boxed{2}$ .

Mamun Abdullah
Aug 28, 2015

As, OABD is a square, so the diagonals of the square AD=OB;

Here, OB= Radius of the circle=2

So, OB=AD=2

It would work also with a rectangle, and it would feel even more surprising that way.

Marta Reece - 4 years, 1 month ago

Maggie Miller
Aug 27, 2015

Since $OABD$ is a square, the diagonals are of equal length (i.e. $AD=OB$ ). Since $OB$ is a radius of the circle, $OB=2$ . Then $AD=OB=\boxed{2}$ .