Mathematics
Can a sector and a segment of a circle coincide? If so, name it.
Geometrical Concepts
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Answer
A sector of a circle is the part of the circular region enclosed by an arc and its two bounding radii.
A segment of a circle is the part of the circular region enclosed by an arc and a chord.
Consider the special case when the chord of a circle is its diameter:
- The diameter divides the circle into two equal halves. Each half is bounded by the diameter (which is the chord) and a semicircular arc. Each half is therefore a semicircular segment.
- The diameter also consists of two radii lying along a single straight line in opposite directions. The region enclosed by these two radii and the semicircular arc is a semicircular sector.
In this case, the sector and the segment refer to the same semicircular region, so they coincide.
∴ Yes, a sector and a segment of a circle can represent the same region in the special case of a semicircle (when the chord is a diameter).
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