Planting Bushes in a Circular Park

In a circular park, a path runs along a diameter, dividing the park into two equal semicircles. The diameter of the park is 14 meters. A gardener plants a rose bush 4 meters away from one edge of the path, towards the center of the park.

If the gardener wants to plant a second bush in a straight line perpendicular to the path and just touching the edge of the park's boundary, determine how far (in meters) from the path the second bush can be planted, rounded to the nearest hundredth.

Use the formula for the radius, which is half of the diameter, and the Pythagorean theorem as necessary.