Question

If AB = 8, and OX = 3 and is the perpendicular bisector of AB, which is the length of the diameter of this circle?

Answer 1

Answer:

  C.  5

Step-by-step explanation:

OXA is a 3-4-5 right triangle, so the circle radius is OA = 5.

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By the Pythagorean theorem,

  AO² = OX² +AX² = 3² +4² = 9 +16 = 25

  AO = √25 = 5 . . . . circle radius

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Comment on Pythagorean triples

The triple of integers (3, 4, 5) is the smallest triple of integers that satisfies the relation of the Pythagorean theorem. The next smallest set is (5, 12, 13). These, and a few other similar triples such as (7, 24, 25) and (8, 15, 17) are often used in algebra and geometry problems because they make the numbers work out nicely. It is worthwhile to learn to recognize these.