F.3 Probability

Question

Please refer to the figure which posted in the following website and answer the question.

http://hk.geocities.com/poonroger12/prob.JPG

The figure shows square ABCD. If point P is drawn inside ABCD at random, find the probability that angle CDP is an acute angle. [Assume that point P will not lie on any boundary lines.] Please show the steps.

Answer 1

Favorite Answer

This explanation may be too long...

When point P is on AD, angle CDP = 90 degrees, which is a right angle, but it cannot happen as point P will not lie on any boundary lines.

When point P is on DC, angle CDP = 0 degree, which is a straight line and cannot happen.

So point P is only restricted under AD and on the right of DC for angle CDP to be acute.

Also, if point P is in the square, it must be under AD and on the right of DC, so the required probability is 100%.