Question

1. choose one of the theorems about chords of a circle and state it using your own words2. create a problem that uses the theorem you explained3. explain how to solve the problem you just did

Answer 1

We have the following:

1. A given chord in a circle is perpendicular to a radius through its center and is a distance less than the radius of the circle.

2. A circle with center C has a radius of 5 units. If a 6-unit chord AB is drawn at a distance D from the center of the circle, determine the value of D.

3.

Given:

Radius = 5 units

Length of chord = 6 units

A radius that meets the chord at center O divides it into two equal parts. Therefore:

AO = OB = 3 units

We can apply the Pythagorean theorem on the resulting triangle COB to determine the distance D, like this:

`\begin{gathered} h^2=a^2+b^2 \\ \\ h=CB=R=5 \\ \\ a=OC=D \\ \\ b=OB=3 \\ \\ \text{ We replacing:} \\ \\ 5^2=D^2+3^2 \\ \\ 25=D^2+9 \\ \\ D^2=25-9 \\ \\ D=√(16) \\ \\ D=4 \end{gathered}`

Therefore, the chord is at a distance of 4 units to the center of the circle.