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प्रश्न
Distance of chord AB from the centre of a circle is 8 cm. Length of the chord AB is 12 cm. Find the diameter of the circle.
उत्तर
Let point O be the center of the circle.
seg OC ⊥ chord AB such that, A-C-B
AC = `1/2` AB ...(The perpendicular drawn from the center of the circle to the chord bisects the chord.)
∴ AC = `1/2 xx 12`
∴ AC = 6 cm
Draw line OA.
In ∆OCA, From Pythagoras theorem,
OA2 = OC2 + AC2
∴ OA2 = 82 + 62
∴ OA2 = 64 + 36
∴ OA2 = 100
∴ OA = `sqrt(100)`
∴ OA = 10 cm
∴ Diameter of circle = `2 xx10`
∴ Diameter of circle = 20 cm
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