Probab / Circles / Triangle

nervesofsteel wrote:IMO D

A) as hyp is the dia of circle .. thus the triangle is a right angle triangle...
thus hyp = 2r , where r is the radius of circle...

So area of circle = pi * r^2
area of triangle = 1/2(sqrt(2)*r) * (sqrt(2)*r)

Thus prob = (Area of circle - Area of triangle)/Area of Circle

r will cancel out from ratio... thus A is sufficient

B) is already sufficient

Thus answer should be D

Musiq wrote:

nervesofsteel wrote:IMO D

A) as hyp is the dia of circle .. thus the triangle is a right angle triangle...
thus hyp = 2r , where r is the radius of circle...

So area of circle = pi * r^2
area of triangle = 1/2(sqrt(2)*r) * (sqrt(2)*r)

Thus prob = (Area of circle - Area of triangle)/Area of Circle

r will cancel out from ratio... thus A is sufficient

B) is already sufficient

Thus answer should be D

You are assuming it's a Right angled Isoceles triangle.

Sure, it is a right angled triangle, but it could be scalene or right. Cannot determine a formula for Area based on r ^2.

kanha81 wrote:A die is rolled randomly on to a circular board with a triangle inscribed in the circle. (All three vertices of the triangle are on the circumference of the circle.) What is the probability that the die comes to rest outside the triangular region?

1.The hypotenuse of the triangle is a diameter of the circle.
2.The radius of the circle is 2 units, and the area of the triangle is 4 square units.

Any idea?