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McGraw Hill Integrated II, 2012 View details

1. Circles and Circumference

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Exercise 55 Page 723

Find the length of the hypotenuse of the inscribed triangle, which is also the diameter of the circle.

40.8

Practice makes perfect

To find the circumference of the circle, we first need to find its diameter. Since one of the sides of the inscribed triangle passes through the center, it is a diameter of the circle. Therefore, the triangle is a right triangle and this side is its hypotenuse.

To find the length of the hypotenuse, we will substitute 5 for a and 12 for b into the Pythagorean Theorem.

a^2+b^2=c^2

SubstituteII

a= 5, b= 12

5^2+ 12^2=c^2

▼

Solve for c

CalcPow

Calculate power

25+144=c^2

AddTerms

Add terms

169=c^2

SqrtEqn

sqrt(LHS)=sqrt(RHS)

sqrt(169)=c

CalcRoot

Calculate root

13=c

RearrangeEqn

Rearrange equation

c=13

Note that since c is the length of the hypotenuse of a right triangle — and the diameter of the circle — we know that it is a positive number. This is why we keep the principal root when solving the equation.