Mathematics Question and Solution
Calculating r, radius of the two congruent circles.
r² = 2²+a²
a = √(r²-4) units.
r² = 1²+b²
b = √(r²-1) units.
c = 2+1+1
c = 4 units.
d = b-a
d = (√(r²-1)-√(r²-4)) units.
Therefore, r, radius of the two congruent circles is;
(2r)² = c²+d²
(2r)² = 4²+(√(r²-1)-√(r²-4))²
4r² = 16+r²-1-2√((r²-1)(r²-4))+r²-4
2r²-11 = -2√((r²-1)(r²-4))
4((r²-1)(r²-4)) = (11-2r²)²
4(r⁴-5r²+4) = 121-44r²+4r⁴
-20r²+16 = 121-44r²
24r² = 105
8r² = 35
r = √(35)/√(8)
r = ¼√(70) units.
r = 2.0916500663 units.
