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a circle O has a chord length of 24 ft anda perpendicular distance from the center of the chord of 5 ft find the radius

Sagot :

Hrishii

Answer:

13 ft

Step-by-step explanation:

  • [tex]l(chord) = 24\: ft[/tex] (Given)

  • [tex]l(perpendicular) = 5\: ft[/tex] (Given)

  • Perpendicular dropped from the center of the circle to the chord bisects the chord.

  • [tex]\implies \frac{1}{2}l(chord) = 12\: ft[/tex]

  • Let the [tex]l(radius)[/tex] be r ft.

  • Radius of the circle, perpendicular to the chord and half of chord forms a right triangle where r represents the hypotenuse. Thus, by Pythagoras Theorem:

  • [tex]r=\sqrt{{[\frac{1}{2}l(chord)]}^2+{[l(perpendicular)]}^2}[/tex]

  • [tex]\implies r=\sqrt{{12}^2+{5}^2}[/tex]

  • [tex]\implies r=\sqrt{144+25}[/tex]

  • [tex]\implies r=\sqrt{169}[/tex]

  • [tex]\implies r= 13\: ft[/tex]
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