Question

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

Answer 1

Answer: The radius is: " 17.692 cm " .
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Note:
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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!).
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