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Chords AB and XY of a circle meet at T. If XT = 4, TY = 6, and AT = 2TB, then what is AB?

Guest Mar 20, 2017
 #1
avatar+7096 
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A rule about intersecting chords says that:

XT * TY = AT * TB             Substitute in what each of these are.

4 * 6 = 2TB * TB               Simplify.

24 = 2(TB)2                       Divide both sides by 2.

12 = (TB)2                         Take the square root of both sides.

√(12) = TB                         Simplify.

2√3 = TB

 

AT = 2TB                           Substitute in 2√3 for TB.

AT = 2(2√3)                        Simplify.

AT = 4√3

 

AB = AT + TB                    Substitute in what we've found for AT and TB.

AB = 4√3 + 2√3                 Simplify.

AB = 6√3 ≈ 10.392

hectictar  Mar 20, 2017

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