a chord of a circle is 4 inches from the center. 
If the diameter of the circle is 10 inches, find 
the length of the chord.

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I can't draw on here, so follow my instructions
and draw it on your paper.

Since the diameter is 10 inches, the radius is 
5 in. Draw a circle with radius 5 inches.  Label 
the center O. 

Draw a radius OA.  Locate point B on OA 4 inches 
from O (and 1 inch from A).

Draw chord CD through B perpendicular to OA.
Draw radii OC and OD.

Triangles OBC and OBD are congruent right triangles.

Use the Pythagorean theorem on right triangle OBC:
OC has measure 5 inches because it is a radius.
OB has meanure 4 inches because that is given. So

OC² = OB² + BC²
 5² = 4² + BC²
 25 = 16 + BC²
  9 = BC²
 Ö9 = BC
  3 = BC

So BC has measure 3 inches.  By congruent right 
triangles, BD also has measure 3 inches.  So
chord CD = BC + BD = 3 in + 3 in = 6 in.

Edwin