B is 34 mm from the center of circle O, which has a radius of 16 mm. Line BP and line BR are tangent segments. Line AC is tangent to circle O at point Q. Find the perimeter of ABC?

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1 Answer
CW
Oct 25, 2017

perimeter #=60# mm

Explanation:

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#BR=sqrt(BO^2-OR^2)=sqrt(34^2-16^2)=sqrt900=30#
as the two tangent segments to a circle from an external point are equal in length, #=> color(red)(BR=BP, AP=AQ, and CR=CQ)#
perimeter of #DeltaABC=AB+BC+AC#
#=AB+BC+AQ+QC#
#=(AB+AQ)+(BC+QC)#
#=> (AB+AP)+(BC+CR)#
#=> BP+BR#
#=30+30=60# mm

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