Question

the radius of a circle is 10.8ft the length of a chord is 12ft what is the approximate distance of the chord from the center of the circle

Answer 1

• Hypotenuse=10.ft
• Half of chord=Base=12/2=6ft

Perpendicular=P=?

Apply Pythagorean theorem

• P²=H²-B²
• P²=10.8²-6²
• P²=80.64
• P=8.97
• P≈9ft

Answer 2

9.0 ft (nearest tenth)

Explanation:

The chord is the base of an isosceles triangle with sides of the radius.

To calculate the approximate distance of the chord from the center of the circle, we need to find the height of this triangle.

`\sf height=\sqrt{s^2-((b)/(2))^2}`

(where s is the side length and b is the base length of an isosceles triangle)

Given:

• s = radius = 10.8 ft
• b = chord = 12 ft

`\begin{aligned}\implies \sf height & =\sqrt{10.8^2-\left((12)/(2)\right)^2}\\ & = √(116.64-36)\\ & = √(80.64)\\ & = 8.979977728...\\ & = 9.0\: \sf ft\:(nearest\:tenth) \end{aligned}`