Mathematics Question and Solution
Notice.
The green circles are congruent (their radius is equal). Let it be r.
Calculating r.
a = (1-r) units.
b = (1+r) units.
c = (1-r-r-r) = (1-3r) units.
It implies;
Observing Pythagoras Rule.
b² = a²+c²
(1+r)² = (1-r)²+(1-3r)²
1+2r+r² = 1-2r+r²+1-6r+9r²
4r = 1-6r+9r²
9r²-10r+1 = 0
Resolving the above quadratic equation observing factorization approach.
9r²-9r-r+1 = 0
9r(r-1)-1(r-1) = 0
(9r-1)(r-1) = 0
Therefore;
r ≠ 1 unit.
r = ⅑ units.
It implies, radius of the green congruent circles is ⅑ units.
