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# can somebody tell me how to find the length of the minor arc

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Director
Joined: 21 Sep 2004
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can somebody tell me how to find the length of the minor arc [#permalink]

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25 Dec 2004, 19:21
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can somebody tell me how to find the length of the minor arc?
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Director
Joined: 07 Nov 2004
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25 Dec 2004, 20:21
A.

Let the center of the circle be point C. We need to find the angle PCQ = x

Then, length of minor arc PQ = 2*pi*r*(x/360) = pi*18*(x/360)

Since PQ || OR angle ORP = RPQ = 35 degrees

Consider the triangle PCR, CP = CR = Radius. Its an isoceles triangle. So, angle CRP = CPR = 35 degrees.

Now consider triangle CPQ,
Angle CPQ = angle CPR + angle RPQ = 35 + 35 = 70 degrees.
So, angle CPQ = CQP = 70 degrees
=> angle PCQ = x = 180 - (70+70) = 40 degrees

So, length of arc = 18*pi*(40/360) = 2*pi

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Manager
Joined: 20 Dec 2004
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25 Mar 2005, 06:46
excellent explanation !!!
_________________

Regards

Subhen

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25 Mar 2005, 06:46
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# can somebody tell me how to find the length of the minor arc

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