May 2021
Problem of the Month

Geometry Problem

In the diagram below, the measure of angle CAE = 60 degrees. The diameter of the circle is 3/8 " and CA and AE are tangents to circle B.

Determine the value of x.

Solution to the Problem:

x = 1/16 ".

Draw segments AD and BC.   You can prove that triangle ABC is a right triangle with a right angle at C and the measure of angle B = 60 degrees and the measure of angle A = 30 degrees.

BC = 3/16 " because it is a radius and therefore half the diameter of 3/8 ".

That makes AB = 3/8 " because the hypotenuse is twice the length of the side opposite 30 degrees.

Then DA = AB + BD = 3/8 + 3/16 = 9/16 ".

So, x = DA - 1/2" = 9/16 - 1/2 = 1/16 ".

Correctly solved by:

1. Veena Mg	Bangalore, Karnataka, India
2. Taylor Balding	Redlands Middle School, Grand Junction, Colorado
3. Colin (Yowie) Bowey	Beechworth, Victoria, Australia
4. Kelly Stubblefield	Mobile, Alabama
5. K. M. Thomas	Mumbai, Maharashtra, India
6. Ivy Joseph	Pune, Maharashtra, India
7. Hari Kishan	Meerut, Uttar Pradesh, India

Send any comments or questions to: David Pleacher