Question

Diameter of a circle is 26 cm and length of a chord of the circle is 24 cm. Find the distance of the chord from the centre.

Answer 1

Let O be the center of the circle and seg PQ is its chord.

seg OR ⊥ chord PQ such that, P-R-Q

PQ = 24 cm

diameter of circle = 26 cm

radius = `1/2 xx26`

= 13 cm

Draw line OP.

∴ OP = 13 cm

∴ PR = `1/2` PQ      ...(Perpendicular drawn from the center of a circle to the chord bisects the chord.)

∴ PR = `1/2 xx 24`

∴ PR = 12 cm

In ∆ORP, From Pythagoras theorem,

OP² = OR² + PR²

∴ 13² = OR² + 12²

∴ 169 = OR² – 144

∴ OR² = 169 – 144

∴ OR² = 25

∴ OR = `sqrt(25)`

∴ OR = 5 cm

∴ The distance of the chord from the centre of the circle is 5 cm.