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Question

If I draw two circles of radius 3cm and 5cm with common centre and draw a line AB such that it is a chord to both circles. Length CD = 4.46 cm. Find the distance of the chords from centre and the length AC.


A

2, 2.35

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B

2.35, 2

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C

3, 2

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D

2.16, 2.35

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Solution

The correct option is A

2, 2.35


CD = 4.46cm

Since OECD

CE=DE=2.23 cm.

Apply Pythagoras Theorem in ΔOEC.

OE2+CE2=OC2

OE2+2.232=9

OE2=4

OE=2

In ΔOEA,

OE2+AE2=OA2

22+AE2=52

AE=4.58 cm

AC = AE - CE

= 2.35 cm


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