6. In the given figure, O is the centre of a circle. Show a sector and a segment. Shade the sector.

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Solution

Sector: A circular sector is a portion enclosed by two radii and an arc.
Segment: A segment of a circle can be defined as a region bounded by a chord and a corresponding arc lying between the chord's endpoints.
$O A C B O$ is a Sector and $A C B A$ is a Segment.

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Q. In the given figure, three sectors of a circle of radius 7 cm, making angles of 60°, 80° and 40° at the centre are shaded. Find the area of the shaded region. [CBSE 2012]

Q. In the following figure, shows a sector of a circle, centre O, containing an angle 0°. Prove that:

(i) Perimeter of the shaded region is

(\tan θ + s e c θ + \frac{πθ}{180} - 1)

(ii) Area of the shaded region is

\frac{r^{2}}{2} (\tan θ - \frac{πθ}{180})

Question 73

In the given figure, O is the centre of the circle,

a) Name all chords of the circle.

b) Name all radii of the circle.

c) Name a chord, which is not the diameter of the circle.

d) Shade sectors OAC and OPB.

e) Shade smaller segment of the circle formed by CP.

Figure shows a sector of a circle, centre O, containing an angle $θ^{\circ}$ . Prove that:

(i) Perimeter of the shaded region is $r (t a n θ + s e c θ + \frac{π θ}{180} - 1)$

(ii) Area of the shaded region is $\frac{r^{2}}{2} (t a n θ - \frac{π θ}{180})$

In the given figure, three sectors of a circle of radius 7 cm, making angles of $60^{\circ}, 80^{\circ} a n d 40^{\circ}$ at the centre are shaded. Find the area of the shaded region.

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6. In the given figure, O is the centre of a circle. Show a sector and a segment. Shade the sector.

Sector: A circular sector is a portion enclosed by two radii and an arc.Segment: A segment of a circle can be defined as a region bounded by a chord and a corresponding arc lying between the chord's endpoints.OACBO is a Sector and ACBAis a Segment.

Sector: A circular sector is a portion enclosed by two radii and an arc.
Segment: A segment of a circle can be defined as a region bounded by a chord and a corresponding arc lying between the chord's endpoints.
$O A C B O$ is a Sector and $A C B A$ is a Segment.