Q. 205.0( 3 Votes )

Find the area of

Answer :

The figure for the above question is



So, arc AB = 44cm, radius, r = BO = AO = 42cm………(i)


We know the length of the arc can be written as



Substituting the values, we get






θ = 60°……(ii)


So, the angle of the minor segment is 60°.


The minor segment can be divided into two as shown in the figure.



So, we know the


area of segment ABX = area of sector AOBX – area of ΔAOB….(iii)


We know,


area of sector AOBX


Substituting the values from equation (i) and equation (ii), we get


area of sector AOBX


area of sector AOBX


area of sector AOBX = 22 × 7 × 6


area of sector AOBX = 924cm2………..(iv)


Now consider ΔAOB, and draw a line AM perpendicular to AB, i.e.,



Here AO = OB,


by RHS congruency ΔAMOΔBMO


Now by CPCT (Corresponding parts of congruent triangles are equal), so AM = MB AB = 2AM………….(v)


Hence M is the mid - point of AB and


AOM = BOM =


Now consider right - angled ΔAMO, we know



Now substituting the corresponding values, we get




But , substituting this value in above equation, we get




OM = 21√3cm…..(vi)


And also, in same triangle,



Now substituting the corresponding values, we get



But ,


substituting this value in above equation, we get




AM = 21cm….(vii)


Now the area of ΔABO




Substituting values from equation (v) and (vi), we get


Area of ΔABO


Substituting values from equation (vii), we get


Area of ΔABO


Cancelling the like terms, we get


Area of ΔABO = 441√3cm2……(viii)


So, from equation (iii), we have


area of segment ABX = area of sector AOBX –area of ΔAOB


Substituting values from equation (iv) and (viii) in above equation, we get


area of segment ABX = (924 - 441√3) cm2


Hence the area of the minor segment of the given circle is (924 - 441√3)cm2


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses