well, of course, the larger circle has radius 1.
Draw a diagram of the upper right quarter of the square. Include half the diagonal of the square, which goes through the centers of the two circles (O and Q), which are tangent at point P.
Draw a vertical diameter of the smaller circle, passing through its center Q, and intersects the side of the square at R.
Draw a small horizontal segment from P to where it intersects the vertical diameter through Q at S.
Adding up the vertical pieces,
OP = 1 (the radius of the larger circle)
PQ = QR = r (the radius of the smaller circle)
SQ = r/√2
1/√2 + r/√2 + r = 1
so,
r = (√2-1)/(√2+1)
a circle of radius 1 is inscribed in a square. A smaller circle is tangent to two sides of the square and the first circle. Determine the radius of smaller circle and larger circle
2 answers
A piece of wire 30 cm long is cut into two pieces. One of these is bent into a circle, and the other is bent into a square enclosing the circle, as shown in the diagram. What is the diameter of the circle? (Remember that the circumference of a circle = 2 pi r.