GSEB Class 6 Maths Solutions Chapter 4 Basic Geometrical Ideas Exercise 4.6

Question 1. From the figure, identify:
(a) the centre of circle
(b) three radii
(c) a diameter
(d) a chord
(e) two points in the interior
(f) a point in the exterior
(g) a sector
(h) a segment
Answer:
In the given figure, we have:
(a) The middle point of the circle is O.
(b) The three lines from the center to the edge of the circle (radii) are: \( \overline{\mathrm{OA}} \), \( \overline{\mathrm{OB}} \), and \( \overline{\mathrm{OC}} \).
(c) A line segment that goes through the center and connects two points on the circle (diameter) is \( \overline{\mathrm{AC}} \).
(d) A line segment connecting two points on the circle (chord) is \( \overline{\mathrm{ED}} \).
(e) The two points found inside the circle are O and P.
(f) The point located outside the circle is Q.
(g) A section of the circle like a slice of pie (sector) is shown as OBA.
(h) A part of the circle enclosed by an arc and a chord (segment) is shown as ED.

Exam Tip: Remember to correctly identify the specific parts of the circle based on their definitions: a radius connects the center to the edge, a diameter passes through the center connecting two edges, and a chord connects two edges without necessarily passing through the center.

Question 2.
(a) Is every diameter of a circle also a chord?
(b) Is every chord of a circle also a diameter?
Answer:
(a) Yes, a diameter is always the longest chord in a circle.
(b) No, not every chord of a circle is also a diameter.
In simple words: All diameters are chords, but only chords that go through the middle of the circle are diameters.

Exam Tip: Understand that a diameter is a special type of chord, specifically the longest one that passes through the circle's center. All other chords do not pass through the center.

Question 3. Draw any circle and mark
(a) it's centre
(b) a radius
(c) a diameter
(d) a sector
(e) a segment
(f) a point in its interior
(g) a point in its exterior
(h) an are
Answer:
In the adjoining figure:
(a) The middle point of the circle is O.
(b) \( \overline{\mathrm{OP}} \) is a line from the center to the edge (radius) of the circle.
(c) \( \overline{\mathrm{AB}} \) is a line that passes through the center and connects two points on the circle (diameter).
(d) OMN (the shaded part) is a section like a slice of pie (sector) of the circle.
(e) AJK (the shaded part) is a part of the circle enclosed by an arc and a chord (segment) of the circle.
(f) The point Q is found inside the circle.
(g) The point L is located outside the circle.
(h) \( \overline{\mathrm{MN}} \) is a curved part of the circle (an arc).

Exam Tip: When drawing and marking parts of a circle, clearly label each component with the correct letter or name to avoid confusion. Pay attention to shading for sectors and segments.

Question 4. Say true or false:
(a) Two diameters of a circle will necessarily intersect.
(b) The centre of a circle is always in its interior
Answer:
(a) Yes, this statement is correct.
(b) Yes, this statement is correct.

Exam Tip: All diameters in a single circle must pass through the center, meaning they will always cross at that specific point. The center is, by definition, an internal point of the circle.