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 view all courses 