Chord \displaystyle \overline{AB} AB is 12 inches from center \displaystyle OO. If the radius has a length of \displaystyle 1515 inches, find the length of chord \displaystyle \overline{AB} AB .

18 inches

Step-by-step explanation:

Given

--- radius

--- distance between chord and the center of the circle

Required

The chord length

See attachment for illustration

First, calculate distance AX using Pythagoras theorem.

This gives:

Collect like terms

Take square roots of both sides

AB is then calculated as:

Where:

So:

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