Question

if the distance of 10cm long chord from centre of the circle 12 cm then what is the the diameter of the circle?​

Answer 1

Diameter of the circle is 26 cm

A 10cm long chord is drawn 12cm away from the centre of the circle.

let radius of the circle is r.

we know, chord is perpendicularly bisected by the radius of the circle.

see figure,

(5cm)² + (12cm)² = r²

⇒25 cm² + 144 cm² = r²

⇒ 169 cm² = (13cm)² = r²

⇒r = 13cm

now, diameter of circle is 2 × 13 = 26cm

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Answer 2

By pythagoras theorm:-

${ab}^{2} = {5}^{2} + {12}^{2} \\ {ab}^{2} = 25 + 144 \\ {ab}^{2} = \sqrt{169} \\ab = 13 \: cm$

thus AB=13 cm

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