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A point P is given outside of a circle Gamma. A tangent from P touches Gamma at T with PT=45. A line from P cuts Gamma at the 2 points A, B. If PA=25, what is the length of PB?

 

 May 15, 2020
 #1
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+1

We  can use  the tangent-secant theorem  that  says that

 

PT^2  = PA  ( PA + BA)

 

45^2  = 25 (25 + BA)

 

2025  = 25^2  + 25BA

 

2025  = 625 + 25BA

 

2025 - 625  = 25BA

 

1600 = 25BA      divide both sides by 25

 

64  = BA

 

So

 

PB  = (PA + BA)  =  (25 + 64)   =   89

 

 

cool cool cool

 May 15, 2020

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