Chords AB and XY of a circle meet at T. If XT = 4, TY = 6, and AT = 2TB, then what is AB?
+9479 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
