Question

The radius of a circle is 13 cm and the length of one of its chords is 10 cm. The distance of the chord from the centre is

(a) 22. cm

(b) 12 cm

(c) $\sqrt{6}9$ cm

(d) 23 cm

Answer 1

The figure is shown below,

OA = 13cm, AB = 10cm,
OC is the line drawn from the centre to the chord.
(Line drawn from centre to the chord is perpendicular to the chord, and bisect the chord)
Hence OC is perpendicular to AB, and AC = 5cm
and △ACO is a right triangle.
so using pythagoras theorem, we get


and the distance from the center to the chord is OC, hence the distance is 12cm
option b is correct