Probab / Circles / Triangle

[kanha81]

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?

[anksgupta]

IMO B

From 1, we cannot calculate the area of triangle or circle, All we can say is that probability will be min, when triangle is right angle isoceles triange. So not suffi

From 2, Since both the areas are given(triange m circle) probibility is
(1-(4/4pi)) So suff.. Hence I feel B

[abhinav85]

IMO B.

What is the OA?

[Musiq]

B here as well.

[nervesofsteel]

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]

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]

Many thanks.

OA is [spoiler][/spoiler]

[nervesofsteel]

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.

Thanks ... it makes sense..

i realized my fault...

[mna123]

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?

Where did you get this question from ? Please let me know. I mean what test is that ? I have not seen such questions any where .. I am no very scared .... Please let me know ....

[ghacker]

the answer is B

If we know the area of the triangle and the area of the circle or ant way of finding out this relation we can find the probability

Prob ( event) = chance that event happen = event / total space =area of figure/ total area