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CBSE Class 10 Answered

OABC is a rhombus whose three vertices A , B  and C LIE ON THE CIECLE WITH CENTRE O.If the radius of the circle is 10 cm, find the area of the rhombus ?
Asked by Vikas | 03 Feb, 2016, 12:18: PM
answered-by-expert Expert Answer

begin mathsize 14px style O A B C space i s space a space r h o m b u s. rightwards double arrow A B equals B C equals O A equals O C equals 10 space c m N o w comma space O A thin space equals O B rightwards double arrow triangle O A B space i s space a n space i s o s c e l e s space t r i a n g l e. S i n c e space d i a g o n a l s space o f space a space r h o m b u s space b i s e c t space a t space r i g h t space a n g l e s comma space A D space perpendicular O B. I n space r i g h t space t r i a n g l e space A B D comma A B squared equals A D squared plus D B squared A D squared equals A B squared minus D B squared equals 10 squared plus 5 squared equals 100 plus 25 equals 75 A D equals 5 square root of 3 space c m A C equals 2 cross times A D equals 2 cross times 5 square root of 3 equals 10 square root of 3 space c m A r e a space o f space r h o m b u s space O A B C equals 1 half cross times A C cross times O B equals 1 half cross times 10 square root of 3 cross times 10 equals 50 square root of 3 space c m squared end style

Answered by | 03 Feb, 2016, 06:07: PM

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