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
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