Hello, oohhoohh!
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: .