Question

I suck at figuring out the radius of a circle :c Can someone help please :(

Answer 1

First question:

The line segment that is 40 ft long is a tangent to the circle, meaning it creates a right angle with the radius that intersects it.

Let $r$ be the radius of the circle.

We have a right triangle where the legs are $r$ and $40$, and the hypotenuse is $(20+r)$

I'm hoping you remember the Pythagorean Theorem because this is going to be an important equation for this problem (and the next).

Let's use the dimensions of the right triangle and create a Pythagorean Theorem truth statement:

$r^2+40^2=(20+r)^2$

Simplify the right side so it's easier to solve

$r^2+1600=400+40r+r^2$

Subtract both sides by r²

$1600=400+40r$

Subtract both sides by 400

$1200=40r$

Divide both sides by 40

$r=30$

The value of r is 30, meaning the radius is 30 feet.

Second question:

Please look at the attached image, it would be too hard to try and describe this in words.

We have a right triangle where the legs have a length of 3.6 and half of the length of KL, which is 4.

The hypotenuse is the radius, x.

Use Pythagorean Theorem's to solve for x

$3.6^2+4^2=x^2$

Simplify

$x^2=28.96$

Use a calculator to take the square root of 28.96

$x=5.3814...$

The image is not complete so I can't see how I have to round it, so here are a few different ways this could be rounded:

• To the nearest tenths: $x=5.4$

• To the nearest hundredths: $x=5.38$

• To the nearest thousandths: $x=5.381$

Answerer's Note:

I'm so sorry this took so long to answer. Let me know if you need any clarifications, thanks!

~ Padoru