Question

prove that chord AB and CD,which are intercepted by 2 circles,are equal

Answer 1

Hey it's easy
In triangle oam
Area of triangle oam= 1÷2 ×om×oa
(where om is base and oa is height )
Now in triangle o1dm
Area of triangle o1dm= 1÷2 × dm × o1d(where dm is base and o1d = height)

Now,
Oa=o1d (radius of equal circles will be equal)
And,
Om=o1m(m is mid point of o and o1d)
This means are of ∆ oam = area ∆ o1dm

Now, we have to do the construction
In ∆ oam from o draw a perpendicular to am
And in ∆ o1dm
From o1d draw a perpendicular to md
Now, again find area of both triangles,
1/2×am×oh=1/2×dm×o1j(the areas are equal because we have proved the areas of both triangles equal)
So this means oh =o1j ( altitude of the triangles equal in areas are equal)
So chord ab = CD because their distance from the center is equal
That is oh = o1j