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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.
Solution
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
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