Ask a Doubt
Request a call back

Join NOW to get access to exclusive study material for best results

CBSE Class 10 Answered

Suppose in a circle of centre O, the radius are joined with the end points of a chord, A and B. Now we have to find the minor segment subtended by the chord. So, we have 
Area of sector - Area of triangle = Area of segment
Now, how to find the area of triangle if it's not an equilateral triangle? Take thita anything besides 60 degree and length of chord and radii from your choice.
Thank you!
Asked by Gourav Barik | 03 Mar, 2015, 08:49: PM
answered-by-expert Expert Answer
C o n s i d e r space t h e space f o l l o w i n g space f i g u r e.
H e r e comma space A r e a space o f space A M B C equals A r e a space o f space t h e space s e c t o r space O A C B minus A r e a space o f space t r i a n g l e space O A B C o n s i d e r space t h e space c i r c l e space o f space r a d i u s comma space 4 square root of 2 space c m comma space a n d space l e n g t h space o f space c h o r d space 8 space c m T h a t comma space O A equals O B equals 4 square root of 2 space c m space a n d space A B equals 8 space c m S i n c e space t h e space p e r p e n d i c u l a r space l i n e space j o i n i n g space t h e space c e n t r e space o f space t h e space c i r c l e space a n d space t h e space c h o r d space b i s e c t s space t h e space c h o r d comma space w e space h a v e comma space A M equals M B equals 4 space c m N o w space c o n s i d e r space t h e space r i g h t space t r i a n g l e B y space a p p l y i n g space P y t h a g o r a s space t h e o r e m comma space w e space h a v e comma O A squared equals A M squared plus O M squared rightwards double arrow O M squared equals O A squared minus A M squared rightwards double arrow O M squared equals open parentheses 4 square root of 2 close parentheses squared minus 4 squared rightwards double arrow O M squared equals 32 minus 16 rightwards double arrow O M squared equals 16 rightwards double arrow O M equals 4 T h u s comma space t h e space a r e a space o f space t h e space t r i a n g l e space O A B equals 1 half cross times A B cross times O M equals 1 half cross times 8 cross times 4 equals 16 space s q. space u n i t s N o w space a r e a space o f space t h e space s e c t o r space w i t h space a n g l e space theta equals 90 degree comma space t h e n space A r e a space o f space O A C B equals fraction numerator theta over denominator 360 degree end fraction cross times straight pi cross times straight r squared rightwards double arrow straight A straight r straight e straight a space straight o straight f space straight O straight A straight C straight B equals fraction numerator 90 degree over denominator 360 degree end fraction cross times straight pi cross times open parentheses 4 square root of 2 close parentheses squared rightwards double arrow straight A straight r straight e straight a space straight o straight f space straight O straight A straight C straight B equals 1 fourth cross times straight pi cross times 16 cross times 2 equals 8 straight pi space sq. units straight A straight r straight e straight a space straight o straight f space straight A straight M straight B straight C equals straight A straight r straight e straight a space straight o straight f space straight t straight h straight e space straight s straight e straight c straight t straight o straight r space straight O straight A straight C straight B minus straight A straight r straight e straight a space straight o straight f space straight t straight r straight i straight a straight n straight g straight l straight e space straight O straight A straight B rightwards double arrow straight A straight r straight e straight a space straight o straight f space straight A straight M straight B straight C equals 8 straight pi minus 16
Answered by Vimala Ramamurthy | 05 Mar, 2015, 11:52: AM

Application Videos

Concept Videos

Multiple Choice Questions Practice Test
Answered Unanswered My Questions My Answers
CBSE 10 - Maths
PQ is a chord of length 8 cm to a circle of radius 5 cm. The tangents P and Q intersect at a point T. Find the length of the tangent TP.
Asked by yalagondanikhil | 16 Apr, 2024, 12:25: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
in the given figure a triangle abc is drawn to circumscribe a circle of radius 3 cm such that the segment bd and dc are respectively of length 6 and 9 cm if the area of traingle abc is 54cm2 then find side ab and ac
question image
Asked by jennyy | 26 Mar, 2022, 08:41: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
3. Two supplementary angles are subtended at the centre by two arcs of a circle of radius 7 cm. Find the total length of these arcs  
Asked by sowmyashreeiyer | 31 Jan, 2022, 11:40: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
From a point P, two tangents PA and PB are drawn to a circle C(0, r).  If OP = 2r, then find ∠𝐴𝑃𝐵. What type of triangle is APB?  
Asked by riazu945 | 16 Jan, 2022, 01:00: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
in the above figure major
question image
Asked by ajabraosable27 | 11 Oct, 2021, 09:28: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
prime factorisation
Asked by amikasangma080 | 11 Oct, 2021, 06:14: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
prove that the tangent at any point of a circle is perpendicular to the radius through the point of contact
Asked by muskanmahek2411 | 08 Oct, 2021, 10:48: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
radious of circle is
Asked by anishasheoran372 | 13 Jul, 2021, 09:33: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
In the adjoining figure, AB is the Diameter of the circle. E is not the centre. Angle ACD = 30°. Find angle x.
question image
Asked by bhilarevishwesh | 21 May, 2021, 08:27: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
Q30
question image
Asked by sangyaswarupa | 16 Mar, 2021, 10:06: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
My Class Videos Tests ₹ Plans Ask a Doubt
Get Latest Study Material for Academic year 24-25 Click here
×