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Question Number 58547 by naka3546 last updated on 24/Apr/19

Commented by naka3546 last updated on 24/Apr/19

find the radius of purple circle in r .

findtheradiusofpurplecircleinr.

Answered by mr W last updated on 24/Apr/19

Commented by mr W last updated on 24/Apr/19

OA=(√((1+r)^2 −r^2 ))−1=(√(1+2r))−1 OB=2−r OB^2 =OA^2 +r^2 (2−r)^2 =((√(1+2r))−1)^2 +r^2 4−4r+r^2 =1+2r−2(√(1+2r))+1+r^2 3r−1=(√(1+2r)) 9r^2 −6r+1=1+2r ⇒r=(8/9)

OA=(1+r)2−r2−1=1+2r−1OB=2−rOB2=OA2+r2(2−r)2=(1+2r−1)2+r24−4r+r2=1+2r−21+2r+1+r23r−1=1+2r9r2−6r+1=1+2r⇒r=89

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