Geometry

grkmurthy · Senior Consultant Joined: 14 Oct 2007 Posts: 37

(1) An arc length of 9* pi equals 3/4th the circumference of a circle. What is the shortest distance between the end points of the arc?

(1) 6√2
(2) 4
(3) 12√2
(4) 9
(5) 3√3

ksvickram · Senior Consultant Joined: 02 Jan 2008 Posts: 29

The answer is 6 * sqrt 2. Here is how to arrive at it.

3/4 of the C = 9 * pi =>
Total Circumference = 12 * pi units.
Thus the radius = 6 units.

Now, Consider a point in the minor arc of the circumference, let it be P and the center of the circle be O. Let the extreme points on the arc be A and B.

Since the length of the manjor arc is 3/4 the of the circumference, the angle sub tended by the major arc at the centre will be M(AB) = 270 degrees.

Thus, the angle sub tended by the minor arc at the centre of the circle (i,e AOB ) is 90 degrees. Now, the r=6. AOB is a right abgled triangle, therefore,we get sqrt of 6^2 + 6^2 = 6 * sqrt 2.

Hope this is right.