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# help!

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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

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