06年數學問題

a(i)The area of OAI = 0.5(ar)
(ii) The area of OAB = The area of OAI + OBI + ABI
[s(s-a)(s-b)(s-c)]^0.5 = 0.5ar + 0.5cr + 0.5br
[s(s-a)(s-b)(s-c)]^0.5 = r(s)
r = [(s-a)(s-b)(s-c)/s]^0.5

b(i) b=(3*3 + 4*4)^0.5 = 5
c = 4
a = 3
s = (3+4+5)/2 = 6
r = [(s-a)(s-b)(s-c)/s]^0.5
=1
圓心=(r,r) = (1,1)
so,
The equation of the circle is
(x-1)^2 + (y-1)^2 = 1