Question

If CD = 4 and AB = 5 and CB = 2, find AD

Answer 1

Every tangent to a circle is perpendicular to its radius. In this case, CB and AD are perpendicular to the tangent line.

Given that both radii are perpendicular to the tangent line, we can deduct that they are parallel, that is, CB is parallel to AD.

If we draw a line through A and B, we get the following

Use the basic proportionality theorem to express a proportion between the segments.

`(CB)/(AD)=(AB)/(CD)`

Then, use the given lengths.

`\begin{gathered} (2)/(AD)=(5)/(4) \\ (2\cdot4)/(5)=AD \\ AD=(8)/(5) \\ AD=1.6 \end{gathered}`

Therefore, AD = 1.6.