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Let \(\overline{XY}\) be a tangent to a circle, and let \(\overline{XBA}\) be a secant of the circle, as shown below. If AX = 15 and XY = 9, then what is AB? Express your answer in simplest fraction form. 

I have found answers 27/5 and 29/3 but those are wrong

thx in advance

 Jul 1, 2020
 #1
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By power of a point, AB = 15 - 15/9 = 40/3.

 Jul 1, 2020
 #2
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That is incorecct sorry. thx anyways. 

Guest Jul 1, 2020
 #3
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The answer is 48/5 or 9.6 in decimal form.

HINT(use tangent secant theorem)

 Jul 1, 2020
 #4
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As the second guest states:  the answer is 9.6.

 

Here is an explanation:  XY · XY  =  XB · XA   (This is the correct example of "power of a point".)

                                            9 · 9  =  XB · 15

                                                81  =  15·XB

                                                XB  =  5.4

 

Since   XB + BA  =  XA

            5.4 + BA  =  15

                     BA  =  9.6

 Jul 1, 2020
 #5
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thx yall!!!

Guest Jul 1, 2020

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