In the circle above, if OA and BC are parallel, and radius

Question

In the circle above, if OA and BC are parallel, and radius OA of the circle is 3, what is the length of minor arc AD?

A)  \frac{3}{2}  Pi
B) 2  Pi
C) \frac{5}{2}  Pi
D) 3  Pi
E) 6  Pi

mau5 · Answer

We know that the length of minor arc AD = length of DT+TA.

Now, length of arc DT =  \frac{120*2\pi*r}{360}   = \frac{1*2\pi*3}{3} = 2*\pi .

Also, the lenght of arc AD<length of semicircle = \pi*r = 3*\pi  . The only option between  2*\pi  and  3*\pi  is C.

fameatop · Answer

Geo_gmat.png As per figure angle TOD will be 120 deg Angle COB = 120 because OB = OC, the corresponding angles will be equal as well Thus Angle OCB = 30 deg Because AO & BC are parallel lines, Angle AOT will be 30 deg Angle AOD = Angle AOT + Angle TOD = 30 + 120 = 150 Now, length of arc AD = \frac{150*2\pi*r}{360} = \frac{5*2\pi*3}{12} = 2.5*\pi . Answer C

TGC · Answer

Attached is the solution :

Since We know that Diameter subtends 90 Degree at any part of circle then

Angle DCB=90

Since Angle DOC=60 and OD=OC=radius then
ODC=OCD=60
Since DCB=90
=>OCD=30
Since OC=OB=Radius
Then BOC=120

Sum of all the angles completing one full circle should be=360

Hence X+120+60+30=360
X=150

Asifpirlo · Answer

<BCD = 90
<BCO = 30 <BOC = 120
OA !! BC
<OBC = <AOB=30

<AOD = 120+30+60 = 210

So minor angle = 360 - 210 = 150

Length of Minor arc = 150/360 * 2pi * 3 = 5/2 pi

In the circle above, if OA and BC are parallel, and radius

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