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

Question

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

vgschakri · Answer

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.

Harley1980 · Answer

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.

GMATinsight · Answer

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

i.e. Radius of Circle, r = 5

For Further steps of Solution, please check the Image attached

bumpbot · Answer

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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.

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