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In a circle with centre O, the line OM is perpendicular to the chord AB, with M on AB…

Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

In a circle with centre $O$ , the line $OM$ is perpendicular to the chord $AB$ , with $M$ on $AB$ . $AM = 8\ \text{cm}$ and $OM = 6\ \text{cm}$ . Find the radius and the length of $AB$ .

Need a reminder? The key ideaShow

The perpendicular from the centre to a chord bisects the chord, and Pythagoras gives $r^2 = d^2 + \left(\dfrac{c}{2}\right)^2$ . Equal chords are equally far from the centre, and chords equally far from the centre are equal. A nearer chord is longer.

The worked solution

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Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

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