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Is the Triangle ABC right angled at C?

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Is the Triangle ABC right angled at C?  [#permalink]

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New post 23 Jun 2015, 03:08
3
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

70% (00:44) correct 30% (00:53) wrong based on 158 sessions

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Is the Triangle ABC right angled at C?

1) AB is not the longest chord that can be drawn in a circle.

2) The Length of AB is seven-fifth the radius of the circle.
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Re: Is the Triangle ABC right angled at C?  [#permalink]

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New post 23 Jun 2015, 03:51
monk16 wrote:
Is the Triangle ABC right angled at C?

1) AB is not the longest chord that can be drawn in a circle.

2) The Length of AB is seven-fifth the radius of the circle.


A right triangle's hypotenuse is a diameter of its circumcircle (circumscribed circle).
The reverse is also true: if one of the sides of an inscribed triangle is a diameter of the circle, then the triangle is a right angled
(right angel being the angle opposite the diameter/hypotenuse).
Image

Is the Triangle ABC right angled at C?

According to the above if ABC is right angled at C, then AB (hypotenuse) must be the diameter of circumscribed circle.

(1) AB is not the longest chord that can be drawn in a circle. Diameter is the longest chord possible in a circle, thus AB is NOT a diameter, therefore ABC is not right angled at C. Sufficient.

(2) The Length of AB is seven-fifth the radius of the circle. If ABC were right angled at C, AB would be a diameter, thus equal to twice the radius of the circle. ABC is not right angled at C. Sufficient.

Answer: D.

Attachment:
2015-06-23_1445.png
2015-06-23_1445.png [ 13.04 KiB | Viewed 2196 times ]

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Re: Is the Triangle ABC right angled at C?  [#permalink]

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New post 23 Jun 2015, 03:59
1
Bunuel wrote:
monk16 wrote:
Is the Triangle ABC right angled at C?

1) AB is not the longest chord that can be drawn in a circle.

2) The Length of AB is seven-fifth the radius of the circle.


A right triangle's hypotenuse is a diameter of its circumcircle (circumscribed circle).
The reverse is also true: if one of the sides of an inscribed triangle is a diameter of the circle, then the triangle is a right angled
(right angel being the angle opposite the diameter/hypotenuse).
Image

Is the Triangle ABC right angled at C?

According to the above if ABC is right angled at C, then AB (hypotenuse) must be the diameter of circumscribed circle.

(1) AB is not the longest chord that can be drawn in a circle. Diameter is the longest chord possible in a circle, thus AB is NOT a diameter, therefore ABC is not right angled at C. Sufficient.

(2) The Length of AB is seven-fifth the radius of the circle. If ABC were right angled at C, AB would be a diameter, thus equal to twice the radius of the circle. ABC is not right angled at C. Sufficient.

Answer: D.

Attachment:
2015-06-23_1445.png


How do we know that C lies on circle and not in circle or out of circle?
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Re: Is the Triangle ABC right angled at C?  [#permalink]

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New post 23 Jun 2015, 04:02
Harley1980 wrote:
Bunuel wrote:
monk16 wrote:
Is the Triangle ABC right angled at C?

1) AB is not the longest chord that can be drawn in a circle.

2) The Length of AB is seven-fifth the radius of the circle.


A right triangle's hypotenuse is a diameter of its circumcircle (circumscribed circle).
The reverse is also true: if one of the sides of an inscribed triangle is a diameter of the circle, then the triangle is a right angled
(right angel being the angle opposite the diameter/hypotenuse).
Image

Is the Triangle ABC right angled at C?

According to the above if ABC is right angled at C, then AB (hypotenuse) must be the diameter of circumscribed circle.

(1) AB is not the longest chord that can be drawn in a circle. Diameter is the longest chord possible in a circle, thus AB is NOT a diameter, therefore ABC is not right angled at C. Sufficient.

(2) The Length of AB is seven-fifth the radius of the circle. If ABC were right angled at C, AB would be a diameter, thus equal to twice the radius of the circle. ABC is not right angled at C. Sufficient.

Answer: D.

Attachment:
2015-06-23_1445.png


How do we know that C lies on circle and not in circle or out of circle?


Original question (I've seen it somewhere) has an image showing that ABC is inscribed in a circle.
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Re: Is the Triangle ABC right angled at C?  [#permalink]

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New post 23 Jun 2015, 04:32
1
Harley1980 wrote:
Bunuel wrote:
monk16 wrote:
Is the Triangle ABC right angled at C?

1) AB is not the longest chord that can be drawn in a circle.

2) The Length of AB is seven-fifth the radius of the circle.


A right triangle's hypotenuse is a diameter of its circumcircle (circumscribed circle).
The reverse is also true: if one of the sides of an inscribed triangle is a diameter of the circle, then the triangle is a right angled
(right angel being the angle opposite the diameter/hypotenuse).
Image

Is the Triangle ABC right angled at C?

According to the above if ABC is right angled at C, then AB (hypotenuse) must be the diameter of circumscribed circle.

(1) AB is not the longest chord that can be drawn in a circle. Diameter is the longest chord possible in a circle, thus AB is NOT a diameter, therefore ABC is not right angled at C. Sufficient.

(2) The Length of AB is seven-fifth the radius of the circle. If ABC were right angled at C, AB would be a diameter, thus equal to twice the radius of the circle. ABC is not right angled at C. Sufficient.

Answer: D.

Attachment:
2015-06-23_1445.png


How do we know that C lies on circle and not in circle or out of circle?


Thank you for an idea of a question. :-D
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Re: Is the Triangle ABC right angled at C?  [#permalink]

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New post 23 Jun 2015, 06:22
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Re: Is the Triangle ABC right angled at C?  [#permalink]

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New post 28 Feb 2018, 16:11
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Re: Is the Triangle ABC right angled at C?   [#permalink] 28 Feb 2018, 16:11
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