Chittagong Higher Secondary 2017#8

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samiul_samin
Posts:1007
Joined:Sat Dec 09, 2017 1:32 pm
Chittagong Higher Secondary 2017#8

Unread post by samiul_samin » Thu Mar 01, 2018 1:20 pm

Screenshot_2018-02-23-14-09-22-1-1.png
Circles of radii $5,5,8$ and $\dfrac mn$ are mutually externally tangents to all the circles.Where $m$ and $n$ are relatively prime positive integers.Find $m+n$.

samiul_samin
Posts:1007
Joined:Sat Dec 09, 2017 1:32 pm

Re: Chittagong Higher Secondary 2017#8

Unread post by samiul_samin » Thu Mar 01, 2018 1:24 pm

Hint
Use Pythagorean theorem
Answer
17
Problem Source
AIME 1997/4
Solution Source

samiul_samin
Posts:1007
Joined:Sat Dec 09, 2017 1:32 pm

Re: Chittagong Higher Secondary 2017#8

Unread post by samiul_samin » Sun Feb 17, 2019 8:50 am

samiul_samin wrote:
Thu Mar 01, 2018 1:20 pm
Screenshot_2018-02-23-14-09-22-1-1.png
Circles of radii $5,5,8$ and $\dfrac mn$ are mutually externally tangents to all the circles.Where $m$ and $n$ are relatively prime positive integers.Find $m+n$.
Screenshot_2019-02-17-08-49-49-1.png

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