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Mathematics

Grade9

Easy

Question

A chord of length 30 cm is drawn at a distance of 8 cm from the center of a circle. Calculate the radius of the circle.

17 cm
33 cm
31 cm
15 cm

The correct answer is: 17 cm

option 1: 17cm is the correct answer

$g i v e n space c h o r d space l e n g t h space equals space 30 c m space comma space a n d space i t space i s space 8 c m space f r o m space t h e space c e n t e r comma i t space b i s e c t space t h e space c h o r d space J P space b e c a u s e space i t space i s space space 8 c m space f r o m space t h e space c e n t e r T h e n comma T h e space l e n g t h space o f space A J space equals space 15 space c m space space M J space w i l l space b e space t h e space r a d i u s space s e e space t h e space f i g u r e comma b y space t h e space p y t h a g o r o u s space t h e o r m M J squared space equals space J A squared space plus M A squared M J squared space equals 15 squared space plus space 8 squared space equals 225 plus 64 M J squared equals 289 S O space M J space left parenthesis R a d i u s space right parenthesis space equals space 17 c m space i s space t h e space a n s w e r$

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