Achord of length 24cm is 13cm from the centre of the circle. caculate the radius of the circle

 The radius is:  " 17.692 cm " .

Note:

The line segments are:   "(r + 13)" and "(r –13)" ; 

24cm / 2 = 12 ; 

(r + 13)(r–13) = 12² = 12 * 12 - 144 ; 

(r + 13)(r–13) = 144 ; 

Note:  (a + b)(c + d) = ac + ad + bc + bd ;

So:  Given:  " (r + 13)(r–13) " ; 

 →  " (r + 13)(r–13) "  =  " (r * r) + (r * -13) + (13*r) + (13* -13) " ; 

                                 =  "  r² + (-13r) + 13r + (-169) " ; 

                                 =  "  r² – 13r + 13r – 169 " ; 

                                 =  r² – 169 ; 

→  r² – 169 = 144 ; 

Add  " 169 " to each side of the equation; 

→ r² – 169 + 169 = 144 + 169 ;

to get:

→ r²  = 313  ;

Take the "positive square root" of EACH SIDE of the equation;
    to isolate "r" on one side of the equation; & to solve for "r" (the "radius") ;

→  √(r²)  =  √313 ;

→  r = 17.6918060129541325 cm. 

round to:  " 17.692 cm " .  (Do not forget the units!).