Length of Arc of Sector
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AB & CD are two equal chords of a circle with centre O which intersect each other at the right angle at point P. If the perpendiculars from the centre to AB and CD meet them at M and N respectively, then MONP is a_______.
square.
kite.
rhombus.
rectangle.
O is a fixed point and P is a point which is at a fixed distance from O. If P moves such that angle between initial and final positions of OP is A < 360∘ then the path taken by P is called
- Maximum length of the chord is 3 times radius.
- Shortest distance of the chord from the centre is the perpendicular from the centre.
- Perpendicular from the centre of a circle bisects the chord.
- Angle subtended by a chord at the major segment is twice the angle subtended at the centre.
[Use π = 3.14]
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The center of a circle bisects each chord on the circle.
- True
- False
A pendulum swings through an angle of 30∘ and describes an arc 8.8 cm in length. Find the length of pendulum in cm.
14.5
15.1
17.3
16.8
For a circle of radius r=10π cm.
Angle subtended by arc θ =12∘ .
What is the length of the arc in cm?
23 cm
13 cm
32 cm
2 cm
- 44 cm
- 32 cm
- 56 cm
- 22 cm
Two line segments AB and CD are taken. Initially, the points A & C and B & D are coincident. The line segment CD is rotated about point D such that CD coincides with AB again, when it covers a distance of x. If the distance covered by C is y, the angle subtended by CD with respect to starting point is θ, then find the relation among x, y and θ. Assume that θ is in degrees.
x = (y × θ)/360
x = (y × θ)/180
y = (x × θ)/360
y = (x × θ)/260
There is a circular swimming pool. There is a bob at the centre of the pool at a distance of 50π m from the pool’s wall. Shyam is standing next to the
wall and holding a thread whose other end is connected to the heavy stationary bob at the centre. Holding the thread Shyam now moves along the wall for 20
seconds and the angle between the initial and final positions of the thread is 12∘. What is Shyam’s speed in metres/minute?
1
10
20
5
The perimeter of a sector of circle with radius 5.7 m is 27.2 m. The length of the arc of sector (in m) is _______.
13.4
15.8
16.9
14.1
The given figure is a sector of a circle of radius 20 cm. Is the perimeter of the sector 61 cm? (Take π=227)
True
False
A circle has radius 5 cm. A section of its circumference has length π cm. What is the angle subtended by this section at the centre?
36∘
45∘
50∘
60∘