06 Nov '04 08:381 edit

A clock has a 3-inch hour-hand and a 4-inch minute-hand. A is the point at the tip of the hour hand, B is the point at the tip of the minute hand, and O is the point at the centre of the clock.

Given that the triangle AOB has integer length sides, find the probability that the triangle is (i) right angled, (ii) isosceles.

If the length of the hour hand is h and the length of the minute hand is m, find the probability that triangle, AOB, with integral length sides, is isosceles. (Assume m > h).

Given that the triangle AOB has integer length sides, find the probability that the triangle is (i) right angled, (ii) isosceles.

If the length of the hour hand is h and the length of the minute hand is m, find the probability that triangle, AOB, with integral length sides, is isosceles. (Assume m > h).