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In the polygon inscribed in circle O above, ∠A=90°. If AB=AE and BC=CD

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Bunuel
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In the polygon inscribed in circle O above, ∠A=90°. If AB=AE and BC=CD [#permalink] New post   15 Jun 2021, 01:30
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In the polygon inscribed in circle O above, ∠A=90°. If AB=AE and BC=CD=DE, as shown above, what is the value of x?

A. 100
B. 105
C. 115
D. 120
E. 150



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Re: In the polygon inscribed in circle O above, ∠A=90°. If AB=AE and BC=CD [#permalink] New post   15 Jun 2021, 03:30
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EB is the diameter of the circle with center O (Say)
Angle AEO and Angle ABO will be 45degrees each
Joining EO, DO and CO will give three Equilateral triangles {Measure of arc= Measure of central angle by the arc = half of inscribed angle}

Angle x = Angle ABO + Angle OBC = 45 + 60 = 105 Degrees

Option (B) is the correct choice IMO

Bunuel wrote:

In the polygon inscribed in circle O above, ∠A=90°. If AB=AE and BC=CD=DE, as shown above, what is the value of x?

A. 100
B. 105
C. 115
D. 120
E. 150



Project PS Butler


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Re: In the polygon inscribed in circle O above, ∠A=90°. If AB=AE and BC=CD [#permalink] New post   20 Jun 2021, 18:11
sumitkrocks wrote:
EB is the diameter of the circle with center O (Say)
Angle AEO and Angle ABO will be 45degrees each
Joining EO, DO and CO will give three Equilateral triangles {Measure of arc= Measure of central angle by the arc = half of inscribed angle}

Angle x = Angle ABO + Angle OBC = 45 + 60 = 105 Degrees

Option (B) is the correct choice IMO

Bunuel wrote:

In the polygon inscribed in circle O above, ∠A=90°. If AB=AE and BC=CD=DE, as shown above, what is the value of x?

A. 100
B. 105
C. 115
D. 120
E. 150



Project PS Butler


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1.png


Hi Sumit can you please explain the part of the equilateral triangle again. Thanks

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Re: In the polygon inscribed in circle O above, ∠A=90°. If AB=AE and BC=CD [#permalink] New post   20 Jun 2021, 19:01
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KetakiUpadhye wrote:
sumitkrocks wrote:
EB is the diameter of the circle with center O (Say)
Angle AEO and Angle ABO will be 45degrees each
Joining EO, DO and CO will give three Equilateral triangles {Measure of arc= Measure of central angle by the arc = half of inscribed angle}

Angle x = Angle ABO + Angle OBC = 45 + 60 = 105 Degrees

Option (B) is the correct choice IMO

Bunuel wrote:

In the polygon inscribed in circle O above, ∠A=90°. If AB=AE and BC=CD=DE, as shown above, what is the value of x?

A. 100
B. 105
C. 115
D. 120
E. 150



Project PS Butler


Subscribe to get Daily Email - Click Here | Subscribe via RSS - RSS


Show Spoiler
Attachment:
1.png


Hi Sumit can you please explain the part of the equilateral triangle again. Thanks

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Hi
the basic principle of a circle

equal chords subtend equal angles at the center, No matter their relative position with the center of the circle


SO angle subtended by DE,DC & CB at center are same and their total equals 180 degree so each of them equals 60 degree

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Re: In the polygon inscribed in circle O above, ∠A=90°. If AB=AE and BC=CD [#permalink]
20 Jun 2021, 19:01
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