Mathematics Question and Solution
Calculating length red.
Let it be x (length BP).
a = ½(2)
a = 1 unit.
a is the radius of the inscribed circle.
b² = 1²+1²
b² = 2
b = √(2) units.
b is half the diagonal of the ascribed square.
c = b-a
c = (√(2-1) units.
d = 2b-c
d =2√(2)-(√(2)-1)
d = 2√(2)-√(2)+1
d = (1+√(2)) units.
Calculating x.
x² = 2²+(1+√(2))²-2*2(1+√(2))cos45
x² = 4+1+2√(2)+2-2(√(2)+2)
x² = 5+2√(2)+2-2√(2)-4
x² = 3
x = √(3) units.
Again, x is BP the required red length.
Or
x² = 2²+(√(2)-1)²-2*2(√(2)-1)cos45
x² = 4+2-2√(2)+1-2(2-√(2))
x² = 7-2√(2)-4+2√(2)
x² = 7-4
x² = 3
x = √(3) units.
x is length BP, the red length.
