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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
