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In the figure shown, ABC is inscribed in the circle and AB is a diameter ... ...

In the figure shown, ImageABC 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) ...

*This question is included in Nova Math - Problem Set J: Geometry

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Replies to This Thread: 1 | ----
In the figure shown, ABC is inscribed in the circle and AB is a diameter ... ... 
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.
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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.
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