What is the radius of the circle that circumscribes the triangle, measure of whose sides is 9, 40 and 41? A. 20 B. 20.5 C. 4 D. 8 E. 45

The given triangle is a right angled triangle whose hypotenuse is 41. In a right angled triangle, Circumradius = 1/2 (hypotenuse) = 20.5

can you elaborate a bit please?

You have lengths of sides 9, 40 and 41. Consider the squares: 9^2 = 81 40^2 = 1600 41^2 = 1681 As you can see, adding 9^2 to 40^2 gives you 41^2, so this is a right triangle, with a 41 hypotenuse. Now, right triangles have a series of properties and we will use the fact that the radius that circumscribes such a triangle is equal to half the hypotenuse (this is a commonly used property- you might want to remember it). This means that the length you are looking for is 41/2 = 20.5.

Now I could recollect this point which I have learnt in my school days... In a right angled triangle, the right angled vertex is the Orthocentre and the midpoint of the hypotenuse is the Circumcentre. Thanq Sureshbala and DanaJ

ven4gmat wrote:Now I could recollect this point which I have learnt in my school days... In a right angled triangle, the right angled vertex is the Orthocentre and the midpoint of the hypotenuse is the Circumcentre. Thanq Sureshbala and DanaJ I think you mean the midpoint of the hypotenuse is the radius.

A midpoint is only a point (in this case the point equally distant from both ends of the hypotenuse), it cannot be a radius. The radius we are looking for is half the length of the hypotenuse.

Do you guys know where i can find all these "triangle inside a circle" rules? Any geometry book will have them? Thanks!

marcusking wrote:I think you mean the midpoint of the hypotenuse is the radius. DanaJ wrote:A midpoint is only a point (in this case the point equally distant from both ends of the hypotenuse), it cannot be a radius. The radius we are looking for is half the length of the hypotenuse. I think this is derived from the rule that a right-triangle within a circle has the diameter as one of its sides or vice versa (or something like this that I can't recollect ) If the diameter is the hypotenuse, then half of it will be the radius.

roger_michael wrote:Do you guys know where i can find all these "triangle inside a circle" rules? Any geometry book will have them? Thanks! Collect all your school math books from standard VI to X and see for the basics in those books. This will help you in almost everything on GMAT CAT Quant