Can anyone help? I don't know what to do with circles.
Two quarter circles of radius 27 are drawn on adjacent corners of a square. A circle is drawn touching these and the bottom side of the square. Find the radius of this circle.
If we connect the center of the smaller circle with the center of either larger circle....this distance = 27 + r
If we draw a segment from the center of the smaller circle perpendicular to the top edge of the square, this distance = 54 - r
Lastly....the distance from where this last segment meets the top edge of the square to the top right vertex of the square = 27
We have a right triangle with legs of 54 - r and 27
And the hypotenuse = 27 + r
So....by the Pythagorean theorem we have that
(54 - r)^2 + 27^2 = (27 + r)^2 simplify
2916 - 108r + r^2 + 729 = 729 + 54r + r^2
2916 - 108r = 54 r
2916 = r (54 + 108)
2916 = 162 r divide both sides by 162
18 = r