Question

Three circles are shown. How many circles tangent to all three of the given circles can be drawn $?$

Short answer

There can be only one such circle which lies at the center of three circles.

Step-by-step solution

Step 1. Given Information.

Three circles are given as shown below,

Step 2. Given details.

The figure shows three circles, two in a row and then one directly above this row.

The three circles seem congruent to each other.

Step 3. Concept used.

It is required to draw circles which are tangent to all the three given circles.

There can be only one such circle which lies at the center of three circles.

The figure is shown below.

Therefore,there can be only one such circle which lies at the center of three circles.