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 |