# In the diagram, CD is tangent to circles A and

In the diagram, CD is tangent to circles A and B, and he circles are tangent to each other. Answer this question If CD = 15 and AB = 17 and CB = 6, find AD = ?

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menerkupvd
Given, In the diagram, CD is tangent to circles A nad B amd the circles are tangent to each other.
CD=15, AB=17 and CB=6
Now,

From the diagram, we can say that CB and BE is the radius of the circle B and AD and AE is the radius of the circle A.
So, $$\displaystyle\therefore{A}{B}={B}{E}+{A}{E}{\left[\because{C}{B}={B}{E}\right]}$$
$$\displaystyle\Rightarrow{17}={C}{B}+{A}{E}$$
$$\displaystyle\Rightarrow{17}={6}+{A}{E}$$
$$\displaystyle\Rightarrow{A}{E}={17}−{6}$$
$$\displaystyle\Rightarrow{A}{E}={11}$$
$$\displaystyle\therefore{A}{D}={A}{E}={11}$$
$$\displaystyle\therefore{A}{D}={11}$$