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10 May 2010, 09:37
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
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55% (02:50) correct
45%
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In the circle above, PQ is parallel to diameter OR, and OR has length 18. What is the length of minor arc PQ?
A. \(2\pi\)
B. \(\frac{9\pi}{4}\)
C. \(\frac{7\pi}{2}\)
D. \(\frac{9\pi}{2}\)
E. \(3\pi\)
Attachment:
Circle.jpg [ 20.23 KiB | Viewed 128944 times ]
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10 May 2010, 16:18
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In the circle above, PQ is parallel to diameter OR, and OR has length 18. What is the length of minor arc PQ?
A. \(2\pi\)
B. \(\frac{9\pi}{4}\)
C. \(\frac{7\pi}{2}\)
D. \(\frac{9\pi}{2}\)
E. \(3\pi\)
The Central Angle Theorem states that the measure of inscribed angle is always half the measure of the central angle.
Let C be the center of the circle.
According to the central angle theorem above \(\angle PCO=2\angle PRO=70\).
As PQ is parallel to OR, then \(\angle QPR = \angle PRO=35\). Again, according to the central angle theorem above \(\angle QCR=2 \angle QPR=70\).
\(\angle PCQ=180-( \angle PCO+ \angle QCR)=180-70-70=40\).
Minor arc \(PQ=\frac{40}{360}*circumference=\frac{2\pi{r}}{9}=2\pi\)
Answer: A.
For more on circle check the circles chapter of Math Book (link in my signature).
06 Jun 2010, 14:56
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I hope this helps. The explanation goes as:
-We know angle CBA=35
-AOB=diameter and hence angle ACB=90
-Thus in triangle ACB, angle CAB=55
-Now in triangle AOC, OA=OC=Radius and thus angle ACO=55 and angle AOC=70.
-Similarly we can find angle DOB=70
-Thus angle COD=180-70-70=40
And length of arc calculation is given in the image=2π
-We know angle CBA=35
-AOB=diameter and hence angle ACB=90
-Thus in triangle ACB, angle CAB=55
-Now in triangle AOC, OA=OC=Radius and thus angle ACO=55 and angle AOC=70.
-Similarly we can find angle DOB=70
-Thus angle COD=180-70-70=40
And length of arc calculation is given in the image=2π
Attachments
IMAG0432.jpg [ 344.09 KiB | Viewed 107033 times ]
