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Let XY be a tangent to a circle, and let XBA be a secant of the circle, as shown below. If AX = 15 and XY = 8, then what is AB?

 

 Jul 9, 2021
 #1
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+1

Here is a similar question:  https://web2.0calc.com/questions/power-of-a-point-question 

 Jul 9, 2021
 #2
avatar+121062 
+1

We  have  this relationship

 

XY^2   =   XB  * AX

 

 8^2  =   XB  (15) 

 

64  =  XB (15)

 

64 / 15   = XB

 

AB =  AX  - XB   =    15   -  64/15  =    (225 - 64)  / 15      =    161/15 

 

 

 

cool cool cool

 Jul 9, 2021
 #3
avatar+1540 
+1

Let XY be a tangent to a circle, and let XBA be a secant of the circle, as shown below. If AX = 15 and XY = 8, then what is AB?

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

AX = 15         XY = 8         BX = x

 

x(AX) = (XY)2          x = 4 4/15

 

AB = AX - x = 10 11/15   

 Jul 9, 2021

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