Question

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

Answer 1

13 ft

Explanation:

• 
  `l(chord) = 24\: ft` (Given)

• 
  `l(perpendicular) = 5\: ft` (Given)

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

• 
  `\implies (1)/(2)l(chord) = 12\: ft`

• Let the
  `l(radius)` 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:

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

• 
  `\implies r=\sqrt{{12}^2+{5}^2}`

• 
  `\implies r=√(144+25)`

• 
  `\implies r=√(169)`

• 
  `\implies r= 13\: ft`