# Problem 5_5

- Author:
- angela

## GeoGebra Construction:

## Problem 5_5

In the following diagram, the three small circles are congruent, and one them touches the chord AB at its midpoint N. Construct the circle (K) by first locating the point of tangency P.

## Solution:

I first constructed the larger circle, O. Then, I constructed segment AB and midpoint N. I created a perpendicular line to AB at point N. And I created point M where the perpendicular line intersected the circle. Then, I constructed the midpoint of segment NM. I created a circle with center as the midpoint of segment MN and radius (1/2)MN. I created two identical circles on either side of this little circle.

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