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Question

The common chord of two intersecting circles c1&c2 can be seen from their centres at the angles of 90and60 respectively. If the distance between their centres is equal to 3+1, then the radii of c1&c2 are

A
3&3
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B
2&22
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C
2&2
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D
22&4
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Solution

The correct option is C 2&2

Let d be the distance between O1O2

In ABO1

AO1B=12AO1C=45

tan45=ABO1BAB=x

r21=x2+x2

r1=x2

In AO2B

AO2B=12AOC=30

tan30=ABOB2AB=(dx)3

(dx)3=xx(3+1)+3+1

x=1

r1=x2=2

r22=x2+(dx)2=1+3=4

r2=2


868440_300544_ans_5824506e272d47d8b4a36afb01e4db59.jpg

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