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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Geometry
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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/(18Ï€)
(1/9)(18Ï€) = PQ
PQ = 2Ï€.
The correct answer is A.
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[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!
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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GMATGuruNY
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myfish wrote:Perhaps my post here will help:GMATGuruNY wrote:
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!
https://www.beatthegmat.com/grockit-circ ... 92556.html
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As a tutor, I don't simply teach you how I would approach problems.
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I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
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As a tutor, I don't simply teach you how I would approach problems.
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