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In OO, OC = 13 and OT = 5.
Find AB.

In OO, OC = 13 and OT = 5. Find AB.-example-1
User Freez
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1 Answer

6 votes

Answer:

AB = 24

Explanation:

You want to know the length of the chord AB in the circle of radius 13 where the distance from the center to the chord is 5.

Right Triangle

Triangle BOT formed by half the chord, the segment to it, and a radius is a triangle with hypotenuse 13 and one leg 5. This tells you it is a {5, 12, 13} right triangle, and the length of half the chord is 12 units.

The length AB is 2·BT = 2·12.

AB = 24

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Additional comment

If you're not familiar with the {5, 12, 13} Pythagorean triple, you can find the length of BT using the Pythagorean theorem:

OB² = OT² +BT²

BT² = OB² -OT² = 169 -25 = 144

BT = √144 = 12

For problems like this it is useful to be familiar with a few of the more common Pythagorean triples: {3, 4, 5}, {5, 12, 13}, {7, 24, 25}, {8, 15, 17}.

In OO, OC = 13 and OT = 5. Find AB.-example-1
User MaxZoom
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