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2. Find the radius of a circle in which a 96 cm chord

is 16 cm closer to the center than an 80 cm chord. Code:

40 E
C * - - - - - - - o - - - - - - - . D
* | .
* |16 .
R * D| 48.
A . - - - * - - - o - - - . - - - * B
. * | . *
. * |x . * R
. * | . *
*
O

The center of the circle is

The radius is: .

The chords are: .

Their distance is

Let

In right triangle .[1]

In right triangle .[2]

Equate [1] and [2]: . x+16)^2 + 40^2 \quad\Rightarrow\quad 32x \:=\:448 \quad\Rightarrow\quad x \:=\:14" alt="x^2 + 48^2 \:=\x+16)^2 + 40^2 \quad\Rightarrow\quad 32x \:=\:448 \quad\Rightarrow\quad x \:=\:14" />

Substitute into [1]: .

. . Therefore: .