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# Trapezoid

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AB and CD are parallel. The length of a chord AB is 7 cm. AD = BC = 3 cm. DC is the diameter of a circle O. Find radius DO.

Dec 28, 2020
edited by Dragan  Dec 28, 2020
edited by Dragan  Dec 28, 2020

#1
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Let the midpoint of AB be M

Let angle COB = theta

Now look at right-angled triangle OMB.

Use triangle MBO to fin an expression for cos(theta)

Use triangle BOC to find an expression for sin(theta)   (Use cosine rule)

No use sine^2(theta) + cos^2(theta) = 1

You should be able to finish it from there.

Note that the answer is an approximation.  Maybe someone will come up with an exact answer.

Dec 28, 2020
edited by Melody  Dec 28, 2020
#2
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AB and CD are parallel. The length of a chord AB is 7 cm. AD = BC = 3 cm. DC is the diameter of a circle O. Find radius DO.

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Let AF be the altitude of a trapezoid ABCD.

AO = DO => r          AB = 7       AD = BC = 3

FO = AB / 2  ==>    FO = 3.5

AD2 - (r - FO)2 = r2 - FO2        ==>        32 - (r - 3.5)2 = r2 - 3.52       ==>  r = 4.5 cm

I "borrowed" Dragan's diagram and added a couple of red lines to make my answer even clearer.

Dec 28, 2020
edited by jugoslav  Dec 28, 2020