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Harder Temple Geometry Problems
Figure 5.6. Find the radius of the small circles, r, in terms of S, the area of the large circle minus the area of the ten small circles.
Example: If S = 234.09, then 2r = 8. . . . A traditional solution can be found on page 167.
Problem 8 This problem was proposed by Suzuki SataroÂŻ and is found on a tablet containing twenty-four problems hung in 1891 at the Shinohasawa shrine of Fukushima city. The tablet measures 273 cm by 98 cm. Let A and B be any two points on one chord of a given circle. Draw four inscribed circles with radii a, b, c, and d, which touch the chord at A and B. (See figure 5.7.) Draw the tangent to two of the inscribed circles, which touches them at points C and D. At this
a e
c
C
A
B
D f
d
b
Figure 5.7. Show that a/b = c/d = e/f.