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Vertices A and B of triangle ABC lie on circle with area 25pi.

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Vertices A and B of triangle ABC lie on circle with area 25pi. [#permalink]

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New post 23 Jun 2015, 06:20
1
4
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A
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D
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Difficulty:

  65% (hard)

Question Stats:

41% (01:36) correct 59% (04:43) wrong based on 58 sessions

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Vertices A and B of triangle ABC lie on circle with area 25pi. Does vertice C of triangle ABC lie on the circle?

1) Angle ACB = 90 degrees
2) Length of AB = 5 cm

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Re: Vertices A and B of triangle ABC lie on circle with area 25pi. [#permalink]

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New post 23 Jun 2015, 09:38
Harley1980 wrote:
Vertices A and B of triangle ABC lie on circle with area 25pi. Does vertice C of triangle ABC lie on the circle?

1) Angle ACB = 90 degrees
2) Length of AB = 5 cm


Should it not be D?

A and B are on a circle and a third point conjoining the two gives and angle 90, by definition has to be a right angle triangle with C on the circle.

Also, I am confused. Even if you look at statement 2, length of AB is the radius and not the diameter (area of circle is 25pi- 5^2pi). In this event, answer would be A.

Please clarify.
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Re: Vertices A and B of triangle ABC lie on circle with area 25pi. [#permalink]

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New post 23 Jun 2015, 09:49
vgschakri wrote:
Harley1980 wrote:
Vertices A and B of triangle ABC lie on circle with area 25pi. Does vertice C of triangle ABC lie on the circle?

1) Angle ACB = 90 degrees
2) Length of AB = 5 cm


Should it not be D?

A and B are on a circle and a third point conjoining the two gives and angle 90, by definition has to be a right angle triangle with C on the circle.

Also, I am confused. Even if you look at statement 2, length of AB is the radius and not the diameter (area of circle is 25pi- 5^2pi). In this event, answer would be A.

Please clarify.


Hello vgschakri

Here is rule about right triangle inscribed in 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 angle being the angle opposite the diameter/hypotenuse)


So hypotenuse of right triangle should be diameter of circle. And in our case we know from task that diameter = 10 and hypotenuse of triangle = 5 so we can infer that vertice C doesn't lie on this circle.

Also you can try to draw circumscribed right triangle with hypotenuse less than diameter of the circle.
Then you clearly see that this is impossible.
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Re: Vertices A and B of triangle ABC lie on circle with area 25pi. [#permalink]

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New post 23 Jun 2015, 11:08
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Harley1980 wrote:
Vertices A and B of triangle ABC lie on circle with area 25pi. Does vertice C of triangle ABC lie on the circle?

1) Angle ACB = 90 degrees
2) Length of AB = 5 cm



Since, Area of Circle = (pi) r^2 = 25 (pi)

i.e. Radius of Circle, r = 5

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Re: Vertices A and B of triangle ABC lie on circle with area 25pi. [#permalink]

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New post 09 Jun 2018, 03:06
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Re: Vertices A and B of triangle ABC lie on circle with area 25pi.   [#permalink] 09 Jun 2018, 03:06
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