Geometry problem 8 by Dhaval Furia

Geometry Level pending

Let T T be the triangle formed by the straight line 3 x + 5 y − 45 = 0 3x + 5y - 45 = 0 and the coordinate axes .

Let the circumcircle of T T have radius of length L L , measured in the same unit as the coordinate axes .

Find the integer closest to L L .


The answer is 9.

Dhaval Furia by Dhaval Furia , 26, India

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Since the triangle is right-angled, the radius of the circumcircle is half the hypotenuse of the triangle :

L = 9 2 + 1 5 2 2 ≈ 8.746 L=\dfrac{\sqrt {9^2+15^2}}{2}\approx 8.746 .

The integral closest to it is 9 \boxed 9 .

0 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...