Question

A circle has two parallel chords of lengths 6 cm and 8 cm. If the chords are 1 cm apart and the center is on the same side of the chords, then diameter of the circle is of length

• A. 5 cm
• B. 6 cm
• C. 8 cm
• D. 10 cm

Answer 1

The correct option is D

10 cm

Let OE = x

OF = x-1

OB = OD ( Radius ) ...(i)

BE = $\frac{1}{2}$ BA = 3 cm

FD = $\frac{1}{2}$ CD = 4 cm

${OB}^2$ = $x^2$ + $3^2$ ....(ii)

${OD}^2$ = ${(x-1)}^2$ + $4^2$ .... (iii)

From (i) , (ii) , (iii)

$x^2$ + $3^2$ = ${(x-1)}^2$ + $4^2$

$x^2$ + 9 = $x^2$ + 1 - 2x + 16

2x = 8

x = 4

Therefore, radius = 5cm and diameter is 10cm