Question

=If CD is tangent to the circle, AB = 1.40 and BC=1.90, what is thelength of CD?

Answer 1

Given:

`\begin{gathered} AB=1.40 \\ BC=1.90 \end{gathered}`

To find the length of CD:

Since, the right triangle ADC,

Using Pythagoras theorem,

`\begin{gathered} AC^2=AD^2+DC^2 \\ (AB+BC)^2=AD^2+CD^2 \\ (1.4+1.9)^2=1.4^2+CD^2\text{ \lbrack{}Since, AD=AB\rbrack} \\ 3.3^2=1.4^2+CD^2 \\ CD^2=3.3^2-1.4^2 \\ CD^2=10.89-1.96 \\ CD^2=8.93 \\ CD=\sqrt[]{8.93} \\ CD\approx2.99\text{ units} \end{gathered}`

Hence, the length is 2.99 units.