Question

AB and CD are two parallel chords of a circle such that AB = 10 cm and CD = 24cm. If the chords are on the opposite sides of the centre and the distance between them is 17 cm, the radius of the circle is

• A. 14 cm
• B. 10 cm
• C. 13 cm
• D. 15 cm

Answer 1

The correct option is C

13 cm

$r^2=x^2+5^2$ [perpendicular from centre bisects the chord]
$r^2=(17-x{)}^2+{12}^2$
Now $x^2+25=(17-x{)}^2+144$ [perpendicular from centre bisects the chord]
$\Rightarrow x=12$




$r^2=144+25$
$r=13cm$