Properties of a Circles
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In the figure, Ac and BD are diametres of the circle with the centre O and AC perpendicular to BD. The chord DF intersects AC at E, DE = 18cm and EF = 7cm, Find the radius of the circle.
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Originally posted by Nathpoop:
In the figure, Ac and BD are diametres of the circle with the centre O and AC perpendicular to BD. The chord DF intersects AC at E, DE = 18cm and EF = 7cm, Find the radius of the circle.
Hi Nathpoop,
The first thing I will like to bring to your attention is that AD = sqrt(AO^2 + OD^2) = sqrt(2r^2), where r is the radius.
Draw a line from A to D, and another from F to O, and you will realise that FE/FO = AE/AD. Thus, 7/r = AE/sqrt(2r^2), which means that 7/sqrt (r^2) = AE/sqrt(2r^2), and AE = 7(sqrt2). Please note that FO is also a radius, hence it is equal to r.
Also, ED/AD = EO/FO, which means 18/sqrt(2r^2) = EO/r, and EO = 18/sqrt2.
Radius = AE + EO =7(sqrt2) + 18/(sqrt2)=7(sqrt2) + 9(sqrt2)=16(sqrt2)
Cheers