Question

What is the radius of the circle shown below? Round to the nearest whole number

Answer 1

Answer:

The circle has a radius of 41 inches

Step-by-step explanation:

Circles

There are certain relations in a circle that help us to identify and calculate some of its characteristics.

The figure shows a circle with three parameters which will lead us to determine its radius. First, we have a chord that measures 80 inches. Since it doesn't go through the center of the circle, it's not the diameter.

But we also have the distance from the center to the chord, making a right angle with it. This makes the chord be divided into two equal parts of 40 inches each.

Now we form a right triangle joining the center to one of the extremes of the chord. The hypotenuse of this triangle is the required radius of the circle. Like every right triangle, this must comply with Pithagora's theorem:

$r^2=x^2+y^2$

where r is the hypotenuse and x, y are the legs or the smaller sides of the triangle. We have determined that x=9, y=40 (or vice-versa, it doesn't matter). Therefore

$r^2=9^2+40^2=1681$

Solving for r

$r=\sqrt{1681}=41\ inches$

The circle has a radius of 41 inches