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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

User Naveen Pantra
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2 Answers

19 votes
19 votes
  • 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
the radius of a circle is 10.8ft the length of a chord is 12ft what is the approximate-example-1
User Georg Heiler
by
2.7k points
21 votes
21 votes

Answer:

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}

the radius of a circle is 10.8ft the length of a chord is 12ft what is the approximate-example-1
User John Russell
by
2.6k points