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ICSE Class 9 Answered

a circle of radius square root of 2 cm is  given.It is divided into 2 segments by a chord of length 2 cm.Prove that the angle subtended by a chord at a point in major segment is 45 degrees ?
Asked by nisha_vini29 | 27 Feb, 2016, 10:52: AM
answered-by-expert Expert Answer
 
 
begin mathsize 14px style Given colon space Radius space of space circle space equals space square root of 2 space cm Length space of space chord space AB space equals space 2 space cm space therefore In space increment AOB comma OA space equals square root of 2 space cm comma space space OB space equals square root of 2 space cm therefore open parentheses OA close parentheses squared plus open parentheses OB close parentheses squared space equals space open parentheses square root of 2 close parentheses squared plus open parentheses square root of 2 close parentheses squared space equals 2 plus 2 equals 4 space cm therefore open parentheses OA close parentheses squared plus open parentheses OB close parentheses squared equals 4 space cm space... left parenthesis 1 right parenthesis AB space equals space 2 space cm therefore open parentheses AB space close parentheses squared equals space 2 squared space equals 4 cm space... left parenthesis 2 right parenthesis Hence comma space from space left parenthesis 1 right parenthesis space and space left parenthesis 2 right parenthesis. open parentheses OA close parentheses squared plus open parentheses OB close parentheses squared equals open parentheses AB space close parentheses squared therefore increment AOB space is space an space isosceles space right space triangle. therefore angle AOB space equals space 90 degree space space Hence space angle space subtended space by space the space chord space AB space at space the space centre space straight O equals 90 degree therefore angle ACB space equals space 90 over 2 equals 45 degree space... left parenthesis Angle space subtended space by space the space chord space at space any space point space on space the space circle space is space half space of space the space angle space subtended space by space the space same space chord space at space the space centre right parenthesis space end style
Answered by Priti Shah | 29 Feb, 2016, 01:03: PM

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