Mathematics
Statement I: The essential component of the sector and the segment of a circle is the arc.
Statement II: A chord which passes through the centre of a circle is its diameter.
Statement I is true but statement II is false.
Statement I is false but statement II is true.
Both Statement I and statement II are true.
Both Statement I and statement II are false.
Answer
Both Statement I and Statement II are true.
Explanation
A sector of a circle is the part of the circular region enclosed by an arc of the circle and its two bounding radii. A segment of a circle is the part of the circular region cut off by a chord, and it is bounded by the chord and an arc. So, in both a sector and a segment, an arc is an essential (common) component. Statement I is true.
A chord is a line segment joining any two points of a circle. When a chord passes through the centre of the circle, it becomes the longest chord — called the diameter — and its length is equal to 2 × radius. So, Statement II is also true.
Hence, option 3 is the correct option.
Related Questions
Statement I: If r is the radius of a circle and l is the length of any chord then 0 ≤ l ≤ 2r.
Statement II: A chord is formed by joining any two points on a circle.
Statement I is true but statement II is false.
Statement I is false but statement II is true.
Both Statement I and statement II are true.
Both Statement I and statement II are false.
Statement I: The terms circle and circular region have the same meaning.
Statement II: The interior of a circle together with its boundary is called the circular region.
Statement I is true but statement II is false.
Statement I is false but statement II is true.
Both Statement I and statement II are true.
Both Statement I and statement II are false.
From the adjoining figure, write
(i) all pairs of parallel lines.
(ii) all pairs of intersecting lines.
(iii) lines whose point of intersection is E.
(iv) collinear points.