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CBSE Class 9 Answered

In a circle of BO  is  of radius=5cm, AB and AC are two chords such that AB=AC=6CM, find the length of the chord BC?
 
Asked by krishan_5 | 02 Mar, 2016, 08:33: AM
answered-by-expert Expert Answer
begin mathsize 12px style ABC space and space OBC space are space isosceles space triangles. space Hence comma space perpendiculars space from space straight A space and space straight O space will space bisect space BC. rightwards double arrow straight O comma space straight D space and space straight A space lie space on space the space same space line space perpendicular space to space BC OA equals radius equals 5 space cm Let space OD equals straight x space cm comma space AD equals 5 minus straight x space cm In space right space triangle space ADB comma space BD equals square root of AB squared minus AD squared end root equals square root of 6 squared minus open parentheses 5 minus straight x close parentheses squared end root... left parenthesis 1 right parenthesis In space right space triangle space BOD comma space BD equals square root of OB squared minus OD squared end root equals square root of 5 squared minus straight x squared end root... left parenthesis 2 right parenthesis From space left parenthesis 1 right parenthesis space and space left parenthesis 2 right parenthesis square root of 6 squared minus open parentheses 5 minus straight x close parentheses squared end root equals square root of 5 squared minus straight x squared end root rightwards double arrow 6 squared minus open parentheses 5 minus straight x close parentheses squared equals 5 squared minus straight x squared rightwards double arrow open parentheses 5 minus straight x close parentheses squared minus straight x squared equals 6 squared minus 5 squared rightwards double arrow 25 minus 10 straight x equals 11 rightwards double arrow straight x equals 14 over 10 equals 7 over 5 therefore BD equals square root of 5 squared minus straight x squared end root equals square root of 5 squared minus open parentheses 7 over 5 close parentheses squared end root equals 24 over 5 BC equals 2 BD equals 2 cross times 24 over 5 equals 48 over 5 end style
Answered by satyajit samal | 02 Mar, 2016, 11:41: AM

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