Advertisements
Advertisements
Question
A chord PQ of a circle of radius 10 cm substends an angle of 60° at the centre of circle. Find the area of major and minor segments of the circle.
Solution
Radius of the circle, r = 10 cm
Area of sector OPRQ
`= 60^@/360^@ xx pir^2`
`= 1/6 xx 3.14 xx (10)^2`
`= 52.33 cm^3`
In ΔOPQ,
∠OPQ = ∠OQP (As OP = OQ)
∠OPQ + ∠OQP + ∠POQ = 180°
2∠OPQ = 120°
∠OPQ = 60°
ΔOPQ is an equilateral triangle.
So, area of ΔOPQ
`= sqrt3/4 xx ("Side")^2`
`= sqrt3/4 xx (10)^2`
`=( 100sqrt3)/4 cm^2`
=43.30 cm2
Area of minor segment PRQ
= Area of sector OPRQ − Area of ΔOPQ
= 52.33 − 43.30
= 9.03 cm2
Area of major segment PSQ
= Area of circle − Area of minor segment PRQ
=π(10)2 − 9.03
=314 − 9.03
= 304.97 cm2
APPEARS IN
RELATED QUESTIONS
In Fig. 8, O is the centre of a circle of radius 5 cm. T is a point such that OT = 13 cm and OT intersects circle at E. If AB is a tangent to the circle at E, find the length of AB, where TP and TQ are two tangents to the circle.
Write True or False. Give reasons for your answers.
If a circle is divided into three equal arcs, each is a major arc.
In the fig. a circle is inscribed in a quadrilateral ABCD in which ∠B = 90° if AD = 23cm,
AB = 29cm and DS = 5cm, find the radius of the circle.
Two parallel chords are drawn in a circle of diameter 30.0 cm. The length of one chord is 24.0 cm and the distance between the two chords is 21.0 cm; find the length of another chord.
Prove that the line segment joining the points of contact of two parallel tangents of a circle, passes through its centre.
The perimeter (in cm) of a square circumscribing a circle of radius a cm, is
Two circles of radii 5 cm and 3 cm intersect at two points and the distance between their centres is 4 cm. Find the length of the common chord
Find the radius of the circle
Diameter = 24 cm
In a circle with centre P, chord AB is parallel to a tangent and intersects the radius drawn from the point of contact to its midpoint. If AB = `16sqrt(3)`, then find the radius of the circle
Two chords AB and AC of a circle subtends angles equal to 90º and 150º, respectively at the centre. Find ∠BAC, if AB and AC lie on the opposite sides of the centre.
