The common chord of two intersecting circles c1&c2 can be seen from their centres at the angles of 90∘and60∘ respectively. If the distance between their centres is equal to √3+1, then the radii of c1&c2 are
Let d be the distance between O1O2
In △ABO1
∠AO1B=12∠AO1C=45∘
tan45∘=ABO1B⟹AB=x
r21=x2+x2
r1=x√2
In △AO2B
∠AO2B=12∠AOC=30∘
tan30∘=ABOB2⟹AB=(d–x)√3
⟹(d–x)√3=x⟹x(√3+1)+√3+1
x=1
r1=x√2=√2
r22=x2+(d−x)2=1+3=4
r2=2