Question

At your imaginary house (in the future), you have a circular patio with a table in the center of the

circle. You are standing 5-feet from the table. You are also 13-feet from a point of tangency. What is
the approximate diameter of the circular patio?

Answer 1

• Perpendicular=P=5ft
• Hypotenuse=H=13ft
• Base=B=radius=?

Apply Pythagorean theorem

`\\ \rm\hookrightarrow B^2=H^2-P^2`

`\\ \rm\hookrightarrow B^2=13^2-5^2`

`\\ \rm\hookrightarrow B^2=12^2`

`\\ \rm\hookrightarrow B=12`

Radius is 12ft

• Diameter=2(12)=24ft

Answer 2

24 ft

Explanation:

This is modelled as a right triangle with height 5 ft and hypotenuse 13 ft

Base of triangle = radius of circle

Find base length using Pythagoras' Theorem: a² + b² = c²

(where a and b are the legs and c is the hypotenuse of a right triangle)

⇒ 5² + b² = 13²

⇒ 25 + b² = 169

⇒ b² = 169 - 25

⇒ b² = 144

⇒ b = √144

⇒ b = 12 ft

Therefore, if b is 12 ft, then the radius is 12 ft.

Diameter of a circle = 2r (where r is the radius)

⇒ diameter = 2 x 12 = 24 ft