Chapter 9, Problem 8CT

To determine

To classify: the given statement as true or false.

Answer to Problem 8CT

The above statement is true.

Explanation of Solution

Given information:

Given statement,

When one chord is further from the center of a circle than another chord, the chord further from the center is the longer of two chords.

Calculation:

Consider statement that one chord is further from the center of a circle than another chord, the chord further from the center is the longer of two chords.

As it is known that, Distance from chord, radius of circle and length of chord form a right angle triangle. So, from Pythagoras theorem square of radius is equal to the sum of square of chord length and the square of distance from chord.

  $\begin{array}{c}{\left(Radius\right)}^2={\left(\text{Distance}\text{from}\text{chord}\right)}^2+{\left(\text{Chord}\text{length}\right)}^2\\ {\left(\text{Chord}\text{length}\right)}^2={\left(Radius\right)}^2-{\left(\text{Distance}\text{from}\text{chord}\right)}^2\end{array}$

It is clear from above equation that if the distance from chord is longer its chord length will be small.

Therefore, if one chord is farther from the center of a circle than another chord, the chord farther from the center is the longer of two chords.