Let the radius of the blue inscribed circle be r.
Calculating r.
(5+r)² = (5-r)² + (5+√(25-10r))²
It implies;
20r = 25+10√(25-10r)+25-10r
30r-50 = 10√(25-10r)
(3r-5)² = 25-10r
9r²-30r+25 = 25-10r
9r² = 30r-10r
9r² = 20r
It implies;
r ≠ 0
r = (20/9) units.
Therefore;
Area of the blue inscribed circle is;
π(20/9)²
= 400π/81 square units.
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