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# AC , the diameter of a circle, is of length 10 cm.B and D ar

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Joined: 30 Jan 2019
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AC , the diameter of a circle, is of length 10 cm.B and D ar  [#permalink]

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15 Feb 2019, 11:40
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AC , the diameter of a circle, is of length 10 cm.B and D are points lying on the circle on either side of AC. BC =6 cm and AD=5cm. Find BD.

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Manager
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WE: Pharmaceuticals (Health Care)
Re: AC , the diameter of a circle, is of length 10 cm.B and D ar  [#permalink]

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15 Feb 2019, 12:46
Because AB is the diagonal of the circle, both triangles ABC and ABD are right angled,
so following Pythagoras,$$AB = 8$$, and $$CD = 5\sqrt{3}$$

as ABCD is a cyclic quadrilateral,
then the ratio of the diagonals $$\frac{AC}{BD} = \frac{(AB*AD+CB*CD)}{(BA*BC+DA*DC)}$$

$$\frac{10}{BD} = \frac{(8*5+6*5\sqrt[]{3})}{(8*6+5*5\sqrt[]{3})}$$

if $$\sqrt[]{3} \approx{1.7}$$, then $$BD \approx{9.9}$$

(is This a GMAT?)
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Re: AC , the diameter of a circle, is of length 10 cm.B and D ar   [#permalink] 15 Feb 2019, 12:46
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