#1**+1 **

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.

Melody Dec 28, 2020

#2**+3 **

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 **

**AD ^{2} - (r - FO)^{2} = r^{2} - FO^{2} ==> 3^{2} - (r - 3.5)^{2} = r^{2} - 3.5^{2} ==> r = 4.5 cm**

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

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jugoslav Dec 28, 2020