Question : $\overline{\mathrm{CT}}$ is a tangent to a circle at the point $\mathrm{T}$ on the circle. Chord $\overline{\mathrm{AB}}$ of the circle is extended to meet the tangent $\overline{\mathrm{CT}}$ at the point $\mathrm{C}$. If $\mathrm{m}(\overline{\mathrm{AB}})=3 \mathrm{~cm}$ and $\mathrm{m}(\overline{\mathrm{BC}})=2.4 \mathrm{~cm}$, find the length (in $\mathrm{cm}$ ) of the tangent $\overline{\mathrm{CT}}$.
Option 1: 4.2
Option 2: 3.6
Option 3: 3.2
Option 4: 4.0
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Correct Answer: 3.6
Solution :
AC = 1.5 + 1.5 + 2.4 = 5.4 cm
According to the chord tangent theorem,
$TC^2=AC\times BC$
⇒ $TC^2=5.4\times 2.4$
⇒ $TC^2=12.96$
⇒ $TC=\sqrt{12.96}$
⇒ $TC=3.6$ cm
Hence, the correct answer is 3.6 cm.
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