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Question
2 circles touch each other externally and a single direct common tangent is drawn from a point O to the two circles as shown in the figure. The length of OA is 20 cm and the length of OB is 30 cm. Length of OR = 16 cm. The image is https://cracku.in/media/radpress/entry_images/Screenshot_2015-04-09_13.16.15.png . Can't we solve this question by OB^2=OS*(OS+2SY). here OS will be 25. hence, 900 = 25 ( 25+2x). so the answer will be 5.5. hence the diameter is 11. now obviously i am wrong. i just cant find out where. can u please help me out? By the way, i am assuming chord OY to be extended till the end of the circle Y.
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Answer
First find the radius of smaller circle, radius is r
OA^2+r^2=(OR+r)^2
gives r=8cm
Then apply similar triangles concept for TraigOAX and TraigOBY
(OA/OB) = (OX/OY)
then OY=36
SY=OY-(OR+2r)
finally, SY=4cm
Answer
Siva already answered it well, I suggest you to Download Geometry CAT formulas pdf, to solve questions from this topic with ease.
