Question

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 .

Answer 1

Answer:

18 inches

Step-by-step explanation:

Given

$r = 15in$ --- radius

$h = 12in$ --- distance between chord and the center of the circle

Required

The chord length

See attachment for illustration

First, calculate distance AX using Pythagoras theorem.

$AO^2 = AX^2 + OX^2$

This gives:

$15^2 = AX^2 + 12^2$

$225 = AX^2 + 144$

Collect like terms

$AX^2 = 225 - 144$

$AX^2 = 81$

Take square roots of both sides

$AX = 9$

AB is then calculated as:

$AB= AX + XB$

Where:

$AX=XB =9$

So:

$AB = 9 + 9$

$AB = 18$