    Question

# Two circles of radii 5 cm and 6 cm with common centre are drawn. There is a line AB such that it is chord to both the circles. CD=8 cm. Find the distance of the chord from centre and the length of AC respectively. A

3 cm, 1.19 cm

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B

2.55 cm, 2.35 cm

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C

3 cm, 2 cm

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D

2.16 cm, 2.35 cm

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Solution

## The correct option is A 3 cm, 1.19 cm Given, CD=8 cm Since, OE⊥CD ⇒CE=DE=CD2=4 cm. Applying Pythagoras Theorem in ΔOEC. OE2+CE2=OC2 ⇒OE2+42=52 ∴OE2=25−16 ⇒OE=3 cm In ΔOEA, OE2+AE2=OA2 ⇒32+AE2=62 ⇒AE2=36−9=27 ⇒AE=√27=3√3=3×1.73=5.19 cm Now, AC=AE−CE=5.19−4=1.19 cm  Suggest Corrections  0    Join BYJU'S Learning Program
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