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Geometry Question help Please?
Two chords of a circle are perpendicular and congruent. Do they have to be diameters? Explain your answer in your journal entry, and include diagrams if you wish.
1 Answer
- ?Lv 74 years ago
No, they don't have to be diameters. In the figure below, there are two examples of pairs of chords which are perpendicular and congruent. The blue pair ARE diameters.
The red pair aren't. I positioned them in a way that made it easy to draw them digitially, but actually one pair of chords which are perpendicular and congruent intersect at any point in the interior of the circle. They both make angles of 45 degrees with the radius that passes through the point of intersection.
The center of the circle is a special case: there are infinite pairs of such chords intersecting there, and all of the chords (since they pass through the center) are diameters.
