Problem Solving

Which of the following lists the number of points at which a circle can intersect a triangle?

(A) 2 and 6 only
(B) 2, 4, and 6 only
(C) 1, 2, 3, and 6 only
(D) 1, 2, 3, 4, and 6 only
(E) 1, 2, 3, 4, 5, and 6

Thanks

alex.gellatly wrote:Which of the following lists the number of points at which a circle can intersect a triangle?

(A) 2 and 6 only
(B) 2, 4, and 6 only
(C) 1, 2, 3, and 6 only
(D) 1, 2, 3, 4, and 6 only
(E) 1, 2, 3, 4, 5, and 6

Thanks

Its E.

>> 1 Point...

Circle passes through one of the vertices of triangle.

>> 2 Point...

Circle intersects one side at 2 points of triangle.

>> 3 Point...

Circle is InCircle or CircumCircle.

>> 4 Point...

Circle intersects one side at 2 points and 2 other sides at 1 point of triangle.

>> 5 Point...

Circle intersects one side at 2 points, 2 other sides at 1 point and a passes though one of the veritices of triangle.

>> 6 Point...

Circle intersects all side at 2 points each of triangle.

Thanks... but I guess I simply don't understand what this questions is even asking. Can someone please explain.

Thanks

alex.gellatly wrote:Thanks... but I guess I simply don't understand what this questions is even asking. Can someone please explain.

Thanks

Hi Alex!

This question has been posted and explained many times. If you do a search on "circle intersect triangle" you'll find a number of detailed solutions, many of which have very informative diagrams.

Happy hunting!

alex.gellatly wrote:Thanks... but I guess I simply don't understand what this questions is even asking. Can someone please explain.

Thanks

Pl. see the attachment.

Shalabh's Quants wrote:

alex.gellatly wrote:Thanks... but I guess I simply don't understand what this questions is even asking. Can someone please explain.

Thanks

Pl. see the attachment.

Your diagram is so clear, now I understand thanks! It's not really that difficult question after all. When I read it.. I was so confused. Thanks!

Which of the following lists the number of points at which a circle can intersect a triangle?

(A) 2 and 6 only
(B) 2, 4, and 6 only
(C) 1, 2, 3, and 6 only
(D) 1, 2, 3, 4, and 6 only
(E) 1, 2, 3, 4, 5, and 6


So the question is basically asking that can all the six points on a circle intersect a triangle or no... Or a limited no. of points on the circle can intersect the triangle.

The attachment clearly shows that all the 6 points very comfortably can intersect the triangle.

There are many figures who are intersected at a specific number of points, and hence this question. No rocket science is asked here...

Hence the correct answer is E...

Hope this helps to understand.