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by myfish » Tue Jun 19, 2012 7:57 pm
I cannot get that one right and I thought I am decent in Geometry.
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by ronnie1985 » Tue Jun 19, 2012 8:34 pm
Angle subtended by arcs are equal.

Angle OQP = Angle ORP = 35 degree

Angle subtended by the arc at the centre is twice the angle made by the intersecting chords.

=>The angle subtended at centre is 70 degree. Since the diameter and other chord are parallel, and if C is the centre of the circle, angle PCO = angle QCR = 70 degree

Hence angle subtended by arc PQ = angle PCQ = 360-70-70-180 = 40

Length of arc = (40/360)*2*pi*9 = 2*pi (A) is the answer.
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by GMATGuruNY » Wed Jun 20, 2012 3:31 am
Image

Since PQ||OR, angle QPR = angle PRO = 35.

An INSCRIBED ANGLE is formed by two chords.
Angles PRO and QPR are inscribed angles.
The degree measurement of an ARC intercepted by an inscribed angle is TWICE the degree measurement of the inscribed angle.
Thus, arc OP = 70° and arc QR = 70°, implying that arc PQ = 40°.

(Degree measurement of arc)/360 = (length of arc)/circumference

Since d=18, we get:
40/360 = PQ/(18π)
(1/9)(18π) = PQ
PQ = 2π.

The correct answer is A.
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by myfish » Thu Jun 21, 2012 8:25 pm
[quote="GMATGuruNY"][url=https://postimage.org/image/922nn5aij/][img]https://s9.postimage.org/922nn5aij/inscribed_35_2.jpg[/img][/url]

Since PQ||OR, angle QPR = angle PRO = 35.

An INSCRIBED ANGLE is formed by two chords.
Angles PRO and QPR are inscribed angles.
The degree measurement of an ARC intercepted by an inscribed angle is TWICE the degree measurement of the inscribed angle.

THIS IS UNCLEAR TO ME. HOW CAN THE ANGLE CHANGE? 35degree is 35degree. Where do the 70degree come from? Why? Thanks so much!
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by GMATGuruNY » Fri Jun 22, 2012 10:01 am
myfish wrote:
GMATGuruNY wrote:Image

Since PQ||OR, angle QPR = angle PRO = 35.

An INSCRIBED ANGLE is formed by two chords.
Angles PRO and QPR are inscribed angles.
The degree measurement of an ARC intercepted by an inscribed angle is TWICE the degree measurement of the inscribed angle.

THIS IS UNCLEAR TO ME. HOW CAN THE ANGLE CHANGE? 35degree is 35degree. Where do the 70degree come from? Why? Thanks so much!
Perhaps my post here will help:

https://www.beatthegmat.com/grockit-circ ... 92556.html
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by Brent@GMATPrepNow » Fri Jun 22, 2012 11:55 am
Here's my solution:
Image

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