SOLUTION: AB is a chord of a circle with centre O and is 40cm long. OD is drawn perpendicular to AB. If OD is 4.5cm in length, find the length of the radius of the circle. (all reasoning mus

Algebra ->  Algebra  -> Circles -> SOLUTION: AB is a chord of a circle with centre O and is 40cm long. OD is drawn perpendicular to AB. If OD is 4.5cm in length, find the length of the radius of the circle. (all reasoning mus      Log On

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Question 12586: AB is a chord of a circle with centre O and is 40cm long. OD is drawn perpendicular to AB. If OD is 4.5cm in length, find the length of the radius of the circle. (all reasoning must be shown). thank you
Answer by kusha(21) About Me  (Show Source):
You can put this solution on YOUR website!
There is a theorm that a perpendicular to a chord from the centre of circle would bisect the chord.
so the length of line segment AD is 20 cm and OD is 4.5 cm. Therefore using pythagoras theorm on triangle ADO we get
AOxAO = ODxOD + ADxAD
therefore AO = Sq Rt(420.25) = the radius of circle