calculating the radius of a circle

O is the centre of the circle. PQ and AB are both chords of the circle with OM perpendicular to PQ and OC perpendicular to AB. OM=5cm, OC=7cm and AB= 48cm. Calculate the radius of the circle.
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1 Answer

The perpendicular from the centre O onto a chord bisects the chord, so AC=CB=24cm, and ABC is an isosceles triangle of height OC. OA=OB=radius by definition of a chord. OC=7cm. The radius is the hypotenuse of right triangle OCA or OCB. Therefore by Pythagoras, radius=√(242+72)=√625=25cm.

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