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Points A, B, and D are on the circumference of a circle with center O.

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Bunuel
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Points A, B, and D are on the circumference of a circle with center O. [#permalink] New post   12 Sep 2018, 00:36
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Points A, B, and D are on the circumference of a circle with center O. If triangle ABO is an equilateral triangle and point D is not on minor arc AB, what is the measure of angle ADB?


A. 90
B. 60
C. 45
D. 30
E. 15
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D
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Re: Points A, B, and D are on the circumference of a circle with center O. [#permalink] New post   12 Sep 2018, 02:50
Bunuel wrote:
Points A, B, and D are on the circumference of a circle with center O. If triangle ABO is an equilateral triangle and point D is not on minor arc AB, what is the measure of angle ADB?


A. 90
B. 60
C. 45
D. 30
E. 15


Angle AOB=60

Angle ADB=Angle subtended by minor arc AB at the circumference=\(\frac{1}{2}\)*Angle subtended by minor arc AB at centre (angle AOB)=60/2=30

Ans. (D)
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Re: Points A, B, and D are on the circumference of a circle with center O. [#permalink] New post   12 Sep 2018, 05:56
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Bunuel wrote:
Points A, B, and D are on the circumference of a circle with center O. If triangle ABO is an equilateral triangle and point D is not on minor arc AB, what is the measure of angle ADB?


A. 90
B. 60
C. 45
D. 30
E. 15


Since the triangle ABO is equilateral therefore the angle drawn at center = 60º

Using the property attached in figure "Angle drawn at centre is always twice the angle drawn at circumference if the angles are drawn by the same arc"

Hence, required angle ADB = (1/2)*Angle AOB = (1/2)*60 = 30º

Answer: option D
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Re: Points A, B, and D are on the circumference of a circle with center O. [#permalink] New post   14 Sep 2018, 09:08
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Bunuel wrote:
Points A, B, and D are on the circumference of a circle with center O. If triangle ABO is an equilateral triangle and point D is not on minor arc AB, what is the measure of angle ADB?


A. 90
B. 60
C. 45
D. 30
E. 15


Since triangle ABO is an equilateral triangle, central angle AOB = 60 degrees and thus minor arc AB is also 60 degrees. Since angle ADB is an inscribed angle intercepting arc AB, angle ADB will be half the measure of arc AB and, therefore, angle ADB = 30 degrees.

Answer: D
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Re: Points A, B, and D are on the circumference of a circle with center O. [#permalink] New post   14 Sep 2018, 11:47
Bunuel wrote:
Points A, B, and D are on the circumference of a circle with center O. If triangle ABO is an equilateral triangle and point D is not on minor arc AB, what is the measure of angle ADB?


A. 90
B. 60
C. 45
D. 30
E. 15


Triangle ABO is an equilateral triangle, means all angles are 60 degrees, including the one at the center ,angle AOB,

All angles made by two points are half the angle made by the points on the center , so d can be anywhere on the major arc the angle will be 30 degrees.


Option D is correct.
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Re: Points A, B, and D are on the circumference of a circle with center O. [#permalink]
14 Sep 2018, 11:47
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