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23 Jun 2015, 06:20
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
44% (01:51) correct
56%
(01:55)
wrong
based on 103
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
Source: self-made
1) Angle ACB = 90 degrees
2) Length of AB = 5 cm
Source: self-made
23 Jun 2015, 09:38
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Harley1980
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.
23 Jun 2015, 09:49
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vgschakri
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.
