9, 40 and 41

[sanju09]

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

[sureshbala]

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

[mjjking]

can you elaborate a bit please?

[DanaJ]

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.

[ven4gmat]

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

[marcusking]

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.

[DanaJ]

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.

[roger_michael]

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

[dendude]

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.

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.

[sanju09]

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