Discussion
In the figure shown, 
ABC is inscribed in the circle and AB is a diameter of the circle. What is the radius of the circle?
*This question is included in Nova Math - Problem Set J: Geometry, question #28
ABC is inscribed in the circle and AB is a diameter of the circle. What is the radius of the circle?
| (A) | 3/2 |
| (B) | ... |
| (C) | ... |
| (D) | ... |
| (E) | ... |
| (F) | ... |
The solution is
Posted: 09/10/2014 08:37
Can't you also solve this problem because you know that it is a 3-4-5 triangle which gives you the diameter? The diameter being half of the radius making that easy to solve. And you don't have to do the Pythagorean theorem.
Posted: 09/10/2014 11:10
Sam, you must be a math whiz. Yes, remembering that a 3-4-5 triangle follows the Pythagorean theorem makes this problem easy to solve.
So, you have to have known 2 things to solve this problem without calculation: 1) a triangle inscribed in a semicircle is a right triangle, and 2) 3-4-5 triangle follows the Pythagorean theorem.
So, you have to have known 2 things to solve this problem without calculation: 1) a triangle inscribed in a semicircle is a right triangle, and 2) 3-4-5 triangle follows the Pythagorean theorem.