Question 1177019: Topic: Similarities (I don't know if proofs is the right section)
A square with 4cm sides is drawn so that its right edge is tangent to a circle..
https://media.discordapp.net/attachments/802751414874537995/821168211176718366/ASSJLEQttoUkAAAAAElFTkSuQmCC.png
Answer by greenestamps(13203)   (Show Source):
You can put this solution on YOUR website!
Call the center of the circle O.
Let A be the top left corner of the square; let B be the point where the circle is tangent to the right side of the square.
Draw diameter containing OB, intersecting the square at point C, which is the midpoint of that side of the square.
Triangle ACO is a right triangle; leg AC is 2 and the hypotenuse is the radius r of the circle, which is what we are to find.
The length of the other leg CO can be determined in terms of the radius r, knowing that BC is 4 and BO is the radius r.
Use the Pythagorean Theorem to solve to find the radius.
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