Question

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Answer 1

A. 3 inches

Explanation:

Triangle ABC is a right angled triangle

Therefore;

Using the Pythagoras theorem then;

AB² + BC² = AC²

but BC = CD = radius

Hence;

4² + r² = (r+2)²

16 + r² = r² + 4r +4

16 - 4 = 4r

12 = 4r

r = 3

Therefore; the radius of the circle is 3 inches

Answer 2

A. 3 Inches

Explanation:

To find the radius of the circle, we need to use the Pythagorean Theorem.

a²+b²=c²

a = r inches

b = AD or 4 inches

Now to get the value of c, we need to consider the measurement of the line AD. The sum of line AD and line DC will be the value of the hypotenuse.

c = r + 2 inches

Now that we have our variables, let's plug them in.

a² + b² = c²

r²+ 4² = (r + 2)²

Now we need to use the FOIL method for r + 2.

r² + 16 = (r + 2)(r + 2)

r² + 16= r² + 2r + 2r + 4

r² + 16 = r² + 4r + 4

Now we can remove r² by subtracting both sides by r², leaving us with:

16 = 4r + 4

Now we subtract 4 from both sides.

4r = 12

Now we divide both sides by 4.

r = 3 inches