Question

Radius of a circle with centre O is 41 units. Length of a chord PQ is 80 units, find the distance of the chord from the centre of the circle.

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 = 80 unit

OP = 41 unit

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

∴ PR = `1/2 xx 80`

∴ PR = 40 unit

In ∆ORP, From Pythagoras theorem,

OP² = OR² + PR²

∴ 41² = OR² + 40²

∴ 1681 = OR² + 1600

∴ OR² = 1681 – 1600

∴ OR² = 81

∴ OR = `sqrt(81)`

∴ OR = 9 unit