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Circle and Arcs

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by kalpak.ranadive » Sat Dec 11, 2010 8:51 am
Hey can anyone let me know how to get this ???

Thanks........

Q: The length of arc AXB is twice the length of arc BZC, and the length of arc AYC is three times the length of arc AXB. What is the measure of angle BCA?


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by minar » Sat Dec 11, 2010 9:34 am
What is the OA?
I got the answer: 40
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by minar » Sat Dec 11, 2010 9:39 am
What is the OA?
I got the answer: 40

Because, the arc AXB is 2/9th of the total arch.
The angle for the full circle is 360 degree, so if we draw an angle from the center (O) connecting A and B, the measurement of angle AOB would be 360*(2/9) = 80 degree.
As a formula: the angle BCA is half of AOB.
So, BCA = 40.

Is it?
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by N:Dure » Sat Dec 11, 2010 3:46 pm
I also got 40, but this way:

The arcs ratio is 1:2:6 (BZC:AXB:AYC) so the angles opposing each of them also have the same ratio 1:2:6

1:2:6 sum 9
x:y:z 180 degrees

y= 180 *2 /9 = 40
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by GaneshMalkar » Sun Nov 04, 2012 8:40 am
x + y + z = 360 degrees

x = 2z ; y = 3x

x + 3x + x/2 = 360; 9x/2 = 360; x = 80 which is Angle (AOB); So A(ACB) = 80/2 = 40
If you cant explain it simply you dont understand it well enough!!!
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