In the figure, ∆ABC is inscribed in the circle. The triangle does not

Question

https://gmatclub.com/forum/download/file.php?id=47238 In the figure, ∆ABC is inscribed in the circle. The triangle does not contain the center of the circle O. Which one of the following could be the value of x in degrees? (A) 35 (B) 70 (C) 85 (D) 90 (E) 105 #GREpracticequestion In the figure, ∆ABC is inscribed in the circle.jpg

Archit3110 · Answer

max value of angle at center is 90* and at points directly above or below center ; it will be >90* 
in this case answer >90* 
IMO E

ScottTargetTestPrep · Answer

We see that angle CAB is an inscribed angle of the circle, and its intercepted arc is BC. Since arc BC is a major arc (i.e., one that is more than 180 degrees) and an inscribed angle is half of the measure of its intercepted arc, then the measure of angle CAB, or x, must be more than 90 degrees. We see that only 105 is more than 90; therefore, choice E is the correct answer.

Answer: E

Mck2023 · Answer

Hi Scott  ScottTargetTestPrep 
Can you please explain how BC is major arc?

Posted from my mobile device

Abhishek009 · Answer

#GREpracticequestion In the figure, ∆ABC is inscribed in the circle.jpg When the vertex of a triangle expands from PR to AC and RQ to AB the vertex expands as a result of which the angle corresponding to it also expands as such it must be > 90 Among the given options only (E) fits in correctly !!

ScottTargetTestPrep · Answer

Solution:

If a triangle is inscribed in a circle such that it does not contain the center of the circle, it must be an obtuse triangle (note: if the center of the circle is on the inscribed triangle, it’s a right triangle, and if the center is inside the triangle, it’s an acute triangle). Since the triangle is obtuse, there must be an obtuse angle and the obtuse angle occurs at the vertex that contains partially the radius when it’s drawn from the vertex to the center of the circle. Notice that when the radius is drawn from B or C to center O, neither BO nor CO is contained in triangle ABC. However, when the radius is drawn from A to center O, AO is partially contained in triangle ABC. Therefore, angle A must be the obtuse angle and hence x > 90. Since 105 is the only number in the given choices that is greater than 90, then 105 is the correct answer.

Answer: E

CrackverbalGMAT · Answer

A chord will divide the circle into two segments i.e major and minor segments.

The angle made by the chord/arc at the center will be twice the angle subtended by it at the circumference ( Major segment).
Also, the reflex angle made at the center will be twice the angle subtended by it at the circumference ( Minor segment).

Attachment:

Capture1.JPG [ 27.16 KiB | Viewed 5774 times ]

If you have a clear overview of this property of circle, this question would be easy.

In the question here, the angle subtended by the chord CB at the minor segment is given as x.

By applying the above property, we can say that reflex angle COB = 2x.

Since reflex angle COB is greater than 180 °, we can conclude that x has to be greater than 90 °.

Analyzing the given answer choices, only answer option E satisfies this condition.

Option E is the right answer.

Thanks,

Clifin J Francis,
GMAT QUANT SME

In the figure, ∆ABC is inscribed in the circle. The triangle does not

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In the figure, ∆ABC is inscribed in the circle. The triangle does not

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