Mathematics Question and Solution
Calculating r, radius of the inscribed circle.
Notice.
The ascribed plane shape is a trapezium.
a = 2r units.
a is the diameter of the inscribed circle.
b²+(2r)² = 10²
b = √(100-4r²) units.
c²+(2r)² = 17²
c = √(289-4r²) units.
d = b+3+c
d = (√(100-4r²)+3+√(289-4r²)) units.
d is AD.
Calculating r.
½(3r)+½(10r)½(17r)+½((√(100-4r²)+3+√(289-4r²))r) = ½(3+(√(100-4r²)+3+√(289-4r²)))*2r
½(33r+√(100-4r²)r+√(289-4r²)r) = ½(6r+2r√(100-4r²)+6r+2r√(289-4r²))
33r+√(100-4r²)r+√(289-4r²)r = ½(6r+2r√(100-4r²)+6r+2r√(289-4r²))
21r+√(100-4r²)r+√(289-4r²)r = 2r√(100-4r²)+2r√(289-4r²)
21r = √(100-4r²)r+√(289-4r²)r
(21r-√(100-4r²)r)² = (289-4r²)r²
441r²-42r²√(100-4r²)+100r²-4r⁴ = 289r²-4r⁴
441r²-42r²√(100-4r²)+100r² = 289r²
541r²-289r² = 42r²√(100-4r²)
252r² = 42r²√(100-4r²)
252 = 42√(100-4r²)
6 = √(100-4r²)
4r² = 100-36
4r² = 64
r² = 16
r = √(16)
r = 4 units.
Again, r is the radius of the inscribed circle.
