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CBSE Class 9 Answered

A circle with centre O in which diameter AB bisects the chord CD. If ED=EC=8cm and EB=4cm, find the radius of the circle.
Asked by Jerlin George | 04 Jan, 2015, 03:34: PM
answered-by-expert Expert Answer
C o n s i d e r space t h e space a b o v e space f i g u r e. L e t space O E equals x space c m space a n d space l e t space O C equals r a d i u s space o f space t h e space c i r c l e equals a space c m I n space O C E comma 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 E squared plus C E squared equals a squared rightwards double arrow x squared plus 8 squared equals a squared.... left parenthesis 1 right parenthesis A l s o space w e space h a v e comma space O E plus E B equals O B equals r a d i u s space o f space t h e space c i r c l e equals a rightwards double arrow x plus 4 equals a rightwards double arrow open parentheses x plus 4 close parentheses squared equals a squared... left parenthesis 2 right parenthesis F r o m space e q u a t i o n s space left parenthesis 1 right parenthesis space a n d space left parenthesis 2 right parenthesis comma space w e space h a v e comma x squared plus 8 squared equals open parentheses x plus 4 close parentheses squared rightwards double arrow x squared plus 64 equals x squared plus 16 plus 8 x rightwards double arrow 64 equals 16 plus 8 x rightwards double arrow 16 plus 8 x equals 64 rightwards double arrow 8 x equals 64 minus 16 rightwards double arrow 8 x equals 48 rightwards double arrow x equals 48 over 8 equals 6 T h u s comma space t h e space r a d i u s space o f space t h e space c i r c l e space i s space a equals x plus 4 equals 6 plus 4 equals 10 space c m
Answered by Vimala Ramamurthy | 04 Jan, 2015, 04:44: PM

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CBSE 9 - Maths
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begin mathsize 12px style Two space chords space AB space and space AC space of space straight a space circle space are space equal. space Prove space that space the space centre space of space the space circle space lies space on space the space angl e space bisector space of space angle BAC. end style
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