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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, OECD

CE=DE=CD2=4 cm.

Applying Pythagoras Theorem in ΔOEC.

OE2+CE2=OC2

OE2+42=52

OE2=2516

OE=3 cm

In ΔOEA,

OE2+AE2=OA2

32+AE2=62

AE2=369=27

AE=27=33=3×1.73=5.19 cm

Now, AC=AECE=5.194=1.19 cm


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