Question

If CD is tangent to the circle, AB = 3.30 and BC=2.80, what is the length of CD?DABс

Answer 1

Given the circle A

CD is tangent to the circle and AD is a radius of the circle

So, CD ⊥ AD

So, the measure of angle ADC = 90

So, the triangle ADC is a right angle triangle

AC is the hypotenuse = AB + BC = 3.30 + 2.80 = 6.10

And AD = AB = the radius of the circle = 3.30

We will use the Pythagorean theorem to find CD

So,

`\begin{gathered} AC^2=AD^2+CD^2 \\ CD^2=AC^2-AD^2 \\ CD^2=6.1^2-3.3^2=26.32 \\ CD=\sqrt[]{26.32}=5.13 \end{gathered}`

So, the answer will be CD = 5.13