Question 1206348
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Apply Thales Theorem to determine we have a right triangle.
Thales Theorem is a special case of the Inscribed Angle Theorem.
This is what your diagram would look like (imagine adding the proper labels)
<img width=300 src="https://upload.wikimedia.org/wikipedia/commons/thumb/4/44/Thales%27_Theorem_Simple.svg/1024px-Thales%27_Theorem_Simple.svg.png">
Image credit:
<a href="https://en.wikipedia.org/wiki/Thales%27s_theorem">https://en.wikipedia.org/wiki/Thales%27s_theorem</a>


radius = 5
diameter = 2*radius = 2*5 = 10
The diameter is the hypotenuse of the right triangle. 
A diameter is a special type of chord that passes through the center. It's the longest chord of the circle.


x = shorter leg of the right triangle
x+2 = longer leg of the right triangle
x > 0 since a negative side length makes no sense.


Due to the Pythagorean Theorem {{{a^2+b^2=c^2}}}, we can say {{{x^2+(x+2)^2 = 10^2}}}


Let's expand things out to solve for x.
{{{x^2+(x+2)^2 = 10^2}}}
{{{x^2+(x+2)(x+2) = 100}}}
{{{x^2+x^2+4x+4 = 100}}}
{{{2x^2+4x+4 = 100}}}
{{{2x^2+4x+4-100=0}}}
{{{2x^2+4x-96=0}}}
{{{2(x^2+2x-48)=0}}}
{{{2(x+8)(x-6) = 0}}}
{{{x+8=0}}} or {{{x-6 = 0}}}
{{{x = -8}}} or {{{x = 6}}}
The quadratic formula is an alternative approach.
Ignore the negative result because we stated x > 0 earlier.


{{{x = 6}}} leads to {{{x+2 = 6+2 = 8}}}


We have a 6-8-10 right triangle.


perimeter = add the sides = 6+8+10 = <font color=red>24 cm</font>
area = 0.5*base*height = 0.5*6*8 = <font color=red>24 square cm</font>
This is one of the fairly rare moments when the perimeter and area are the same value (except for the differing unit types of course).
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