Question

计算r²+(2√2r-R+2r)²=(R-r)²,r/R?

Answer 1

²+(2√2r-R+2r)²=(R-r)²

(R-r)²-(2√2r-R+2r)²=r²

(2√2+1)r*(-2√2r-3r+2R)=r²

-(2√2+1)(2√2+3)r+2(2√2+1)R=r

2(2√2+1)R=[(2√2+1)(2√2+3)+1]r

2(2√2+1)R=(12+8√2)r

r/R=(2√2+1)/(4√2+6)=(2√2+1)(2√2-3)/2(2√2+3)(2√2-3)=(4√2-5)/2