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प्रश्न
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.
उत्तर
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.
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