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<div>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&nbsp;</div> <div>Area of sector - Area of triangle = Area of segment</div> <div>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.</div> <div>Thank you!</div>
Asked by Gourav Barik | 03 Mar, 2015, 08:49: PM
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
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