wu :: forums - Print Page


    
      
        wu :: forums
        (http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/YaBB.cgi)
      

        riddles >> medium >> japanese temple geometry 3
        
(Message started by: klbarrus on Jul 27^th, 2002, 11:13pm)

Title: japanese temple geometry 3
Post by klbarrus on Jul 27^th, 2002, 11:13pm

1) r1, radius of the large inscribed circle
drop a line segment from center of c1, use right triangles:

(a-r1)^2 = r1^2 + (a/2)^2

which solves to r1 = 3a/8

2) r2, radius of the small inscribed circle
drop a line segment from center of c2, use right triangles
(a-r2)^2 = r2^2 + x^2 (x = length of dropped segment)
or x^2 = a^2 - 2ar2
call y = length of bottom segment (a = y + r2)
(a + r2)^2 = x^2 + y^2
sub in:
a^2 + 2ar2 + r2^2 = a^2 - 2ar2 + a^2 - 2ar2 + r2^2
a^2 = 6ar2

or r2 = a/6