Congratulations James Page of Hethersett High School, Norwich on your solution to this question. Again there are many possible methods of showing that the radius of the circle is equal to the side of the square.

The blue line OD is a diameter of the circle and a line of symmetry.

ÐEDC = 150^° and \triangle ECD isosceles so ÐCED = ÐCDE = 15^°.

Now ÐOED = 30^° so ÐOEC = ÐOED - ÐCED = 15^° and hence the red line EC is a line of symmetry for the quadrilateral OEDC proving that the radius of the circle, OC is equal in length to the side of the square.