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Find the radius of the circle.

 

 Apr 28, 2022
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We can use the intersecting chord theorem

 

Let r be the radius

 

Let BP  = r + 5

Let AP = r - 5

Let PC  = sqrt (r^2 + 5)

 

So

PQ * PC   = BP * AP

 

2sqrt [ r^2 +5^2 ]  =  (r + 5) (r -5)

 

2sqrt [ r^2 + 5^2 ]  = r^2  - 25          square both sides

 

4 [ r^2 + 5^2 ] =  r^4  - 50r^2  + 625

 

4r^2  + 100  = r^4  - 50r^2 + 625

 

r^4 - 54r^2 + 525  =  0          complete the square on r

 

r^4  -  54r^2  +  729   =  -525 + 729

 

(r^2  - 27)^2  =  204        take the square root of both sides

 

r^2 - 27 =   sqrt (204)

 

r^2=  sqrt (204)  +  27  

 

r =  sqrt [  2sqrt 51) + 27 ] ≈ 6.43

 

cool cool cool

 Apr 28, 2022

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