Mathematics Question and Solution
Diameter of circle Z will be;
½(Diameter of the ascribed circle - length of the inscribed square)
= ½(√(16²+16²) - 16)
= ½(16√(2)-16)
= (8√(2)-8) cm
The radius of circle Z will be;
½ the diameter of circle Z.
= ½(8√(2)-8)
= (4√(2)-4) cm.
Radius of circle X will be;
2(area triangle with height r cm and base 16 cm) + Area triangle with height r cm and base 16√(2) cm = Area triangle with height and base 16 cm respectively.
2*½*16r + ½*16√(2)r = ½*16²
16r + 8√(2)r = 128
Dividing through by 8.
2r+√(2)r = 16
(2+√(2))r = 16
r = 16/(2+√(2)) cm.
Or
R1 is;
½*½(16√(2) - 16) cm
= (4√(2)-4) cm
R2 is;
16r + 16r + 16√(2)r = 16²
Where r = R2
Therefore;
(32+16√(2))r = 16²
(2+√(2))r = 16
r = 16/(2+√(2)) cm
R2 = 16/(2+√(2)) cm
