Hi MATNTRNG,

First, construct the bisector of the angle.

This is the blue line in the attachment.

Then draw a line from the point of intersection of the 2 given lines to the given point (the red one).

Next, draw any circle with centre on the bisector (the purple one).

Then draw the green line from the centre of this circle to the point where the circle intersects the red line.

A parallel line from the given point to the angle bisector locates the centre of

one of the required circles.

It is simply an enlargement.

To get the other one, join the centre of the purple circle to the 2nd point

of contact with the red line and draw a parallel line from

the given point to the angle bisector.