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avatar+1633 

Two tangents $\overline{PA}$ and $\overline{PB}$ are drawn to a circle, where $P$ lies outside the circle, and $A$ and $B$ lie on the circle.  The length of $\overline{PA}$ is $3,$ and $AB$ has a length of 8.  Find the radius of the circle.

 Jan 16, 2025
 #1
avatar+130317 
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If we look at triangle BPA....note that BP = AP  = 3 and AB  = 8

 

But   BP + AP  <  AB which, by the triangle inequality, is impossible 

 

cool cool cool

 Jan 17, 2025

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