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CBSE Class 9 Answered

Please Explain NCERT Textbook, exercise 10.4 , Q5 and Q6.
Asked by Radha Pandey | 05 Jan, 2015, 01:29: PM
answered-by-expert Expert Answer
Q5.Three girls Reshma, Salma and Mandip are playing a game by standing on a circle of radius 5 m drawn in a park. Reshma throws a ball to Salma, Salma to Mandip, Mandip to Reshma. If the distance between Reshma and Salma and between Salma and Mandip is 6 m each, what is the distance between Reshma and Mandip?

Draw perpendiculars OA and OB on RS and SM respectively.
Let R, S and M be the position of Reshma, Salma and Mandip respectively.
 
 
                                    
 OA and OB are the perpendiculars from the centre to the chord RS and SM.
 
Since the perpendicular from the centre bisects the chord, we have,
 
   AR = AS =  = 3cm
   OR = OS = OM = 5 m     (radii of circle)
    In ytriangle OAR
    OA2 + AR2 = OR2             
    OA2 + (3 m)2 = (5 m)2
    OA2 = (25 - 9) m2 = 16 m2
    OA = 4 m                               
    We know that in an isosceles triangle altitude divides the base, so in RSM
    RCS will be of 90o and RC = CM             
    Area of ORS =   OARS    
Now consider the triangle ORS with OS as base. Then RC is the altitude of the triangle ORS.
 
A r e a space o f space t h e space t r i a n g l e space O R S equals 1 half cross times b a s e cross times a l t i t u d e equals 1 half cross times O S cross times R C
 
Therefore, 
A r e a space o f space t h e space t r i a n g l e space O R S : 1 half cross times O S cross times R C equals 1 half cross times R S cross times O A rightwards double arrow 1 half cross times O S cross times R C equals 1 half cross times 6 cross times 4 rightwards double arrow O S cross times R C equals 6 cross times 4 rightwards double arrow 5 cross times R C equals 6 cross times 4 rightwards double arrow R C equals fraction numerator 6 cross times 4 over denominator 5 end fraction rightwards double arrow R C equals 4.8 space m rightwards double arrow R M equals 2 R C equals 2 cross times 4.8 equals 9.6 space m T h u s space t h e space d i s tan c e space b e t w e e n space R e s h m a space a n d space M a n d i p space i s space 9.6 space m
 
Answered by Vimala Ramamurthy | 06 Jan, 2015, 10:22: AM

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