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

Question

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

Team Careers360 · Accepted Answer

Correct Answer: 3.6

Solution :
AC = 1.5 + 1.5 + 2.4 = 5.4 cm
According to the chord tangent theorem,
$TC^2=AC imes BC$
⇒ $TC^2=5.4 imes 2.4$
⇒ $TC^2=12.96$
⇒ $TC=\sqrt{12.96}$
⇒ $TC=3.6$ cm
Hence, the correct answer is 3.6 cm.

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Question : CT― is a tangent to a circle at the point T on the circle. Chord AB― of the circle is extended to meet the tangent CT― at the point C. If m(AB―)=3 cm and m(BC―)=2.4 cm, find the length (in cm ) of the tangent CT―.Option 1: 4.2Option 2: 3.6Option 3: 3.2Option 4: 4.0

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