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by kvcpk » Sun Aug 08, 2010 5:09 am
rahulsaxena8 wrote:Image
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Let the centre of the circle be A.
angle(OAP) = 70 Since angle(ORP) = 35
Hence angle(APQ) = 70 Since OR and PQ are parallel.
In triangle PAQ, PA = AQ
Hence Angle(PQA) = 70
Hence angle(PAQ) = 180-70-70 = 40
Radius = 18/2 = 9
Length of PQ arc = 40/360 * 2 * pi * 9
Hence length = 2Pi

Hope this helps!!
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by rahulsaxena8 » Sun Aug 08, 2010 5:18 am
thanks for the quick and detailed reply :D
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by kvcpk » Sun Aug 08, 2010 5:35 am
rahulsaxena8 wrote:thanks for the quick and detailed reply :D
You are welcome :)
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by gmatrant » Sun Aug 08, 2010 9:48 am
can you please explain how is OAP 70
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by kvcpk » Sun Aug 08, 2010 9:57 am
gmatrant wrote:can you please explain how is OAP 70
The angle at the centre of a circle is twice the angle at the circumference if both angles stand on the same arc. This is called the Angle at Centre Theorem.

Refer to this link for proof:
https://www.mathsteacher.com.au/year10/c ... e/circ.htm

Hence Angle(OAP) = angle(ORP) * 2

Hope this helps!!
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by rahul goyal » Mon Aug 09, 2010 11:46 pm
kvcpk wrote:
gmatrant wrote:can you please explain how is OAP 70
The angle at the centre of a circle is twice the angle at the circumference if both angles stand on the same arc. This is called the Angle at Centre Theorem.

Refer to this link for proof:
https://www.mathsteacher.com.au/year10/c ... e/circ.htm

Hence Angle(OAP) = angle(ORP) * 2

Hope this helps!!
Thank you very much kvcpk. for your explanation i understand the procedure.
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by alivapriyada » Tue Aug 10, 2010 1:49 am
Let the centre of the circle be A.
angle(OAP) = 70 Since angle(ORP) = 35
Hence angle(APQ) = 70 Since OR and PQ are parallel.
In triangle PAQ, PA = AQ
Hence Angle(PQA) = 70
Hence angle(PAQ) = 180-70-70 = 40
Radius = 18/2 = 9
Length of PQ arc = 40/360 * 2 * pi * 9
Hence length = 2Pi

Hope this helps!!
I didn't get why angle(PQA)=70???
Would you please explain??
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by kvcpk » Tue Aug 10, 2010 2:34 am
alivapriyada wrote:
Let the centre of the circle be A.
angle(OAP) = 70 Since angle(ORP) = 35
Hence angle(APQ) = 70 Since OR and PQ are parallel.
In triangle PAQ, PA = AQ
Hence Angle(PQA) = 70
Hence angle(PAQ) = 180-70-70 = 40
Radius = 18/2 = 9
Length of PQ arc = 40/360 * 2 * pi * 9
Hence length = 2Pi

Hope this helps!!
I didn't get why angle(PQA)=70???
Would you please explain??
PA and AQ are radii. Hence they are equal.
Therefore triangle PAQ is isoceles.
Hence, angle(PQA)=angle(APQ) = 70

Hope this helps!!
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