AB and CD are two parallel chords of a circle lying on the oppos

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4.

AB and CD are two parallel chords of a circle lying on the opposite side of the centre and the distance between them is 17cm. The length of AB and CD are 10 cm and 24 cm, respectively. The radius (in cm) of the circle is

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A.

13

Let the radius of circle be r cm.

AB = 10 cm and CD = 24 cm
In increment ONA,        left parenthesis OA right parenthesis squared space equals space left parenthesis ON right parenthesis squared plus space left parenthesis AN right parenthesis squared space space 
                         straight r squared space equals space left parenthesis ON right parenthesis squared space plus space left parenthesis 5 right parenthesis squared
                     ...(i)
In increment OMC comma         left parenthesis OC right parenthesis squared equals space space left parenthesis OM right parenthesis squared space plus space left parenthesis 12 right parenthesis squared
                          straight r squared space equals space left parenthesis 17 minus ON right parenthesis squared space plus space left parenthesis 12 right parenthesis squared           ...(ii)
Solving Eqs. (i) and (ii),
                          straight O space equals space left parenthesis 17 minus ON right parenthesis squared minus left parenthesis ON right parenthesis squared plus left parenthesis 12 right parenthesis squared minus left parenthesis 5 right parenthesis squared
rightwards double arrow               289 plus left parenthesis ON right parenthesis squared space minus 34 left parenthesis ON right parenthesis minus left parenthesis ON right parenthesis squared plus 44 minus 25 space equals space 0
rightwards double arrow                289 plus 144 minus 25 space equals space 34 space cross times space ON
therefore                                     ON space equals space 408 over 34 space equals space 12 space cm
From Eq. (i),  straight r squared space equals space left parenthesis 12 right parenthesis squared plus space left parenthesis 5 right parenthesis squared space equals space 144 plus 25 space equals space 169
therefore                    r = 13 cm
                          

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