If two parallel chords of length 12 cm each and ‘x’ metres apart
If two parallel chords of length 12 cm each and ‘x’ metres apart are drawn on either side of the centre of a circle then the radius of the circle is equal to.
A. <span class="math-tex">\(\sqrt {36 + \frac{{{{\rm{x}}^2}}}{4}} \)</span>
B. <span class="math-tex">\(\sqrt {36 + {{\rm{x}}^2}} \)</span>
C. 6 + x
D. None of these
Please scroll down to see the correct answer and solution guide.
Right Answer is: A
SOLUTION
Consider the figure as shown above,
The line passing through the center of the circle is the perpendicular bisector of the chord.
⇒ AE = AB/2 = 12/2 = 6 cm
The distance of chords of the same length from the center of a circle is same.
⇒ OE = EF/2 = x/2
Consider ∆AOE,
AO2 = AE2 + OE2
⇒ AO = \(\sqrt {{6^2} + {{\left( {\frac{{\rm{x}}}{2}} \right)}^2}} \)
\(\therefore AO = \sqrt {36 + \frac{{{x^2}}}{4}} \)
⇒ The radius of the circle = \(\sqrt {36 + \frac{{{x^2}}}{4}} \)
