Question

Two circle with centres A and B touch each other internally . Another circle touches the larger scale externally at the point X and the smaller circle externally at the point Y . if O be the centre of that circle , let us prove that that AO + BO is constant​

Answer 1

Answer:

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Answer 2

Step-by-step explanation:

Let the circle with Centre A touches the circle with Centre B internally at the circle with Centre B internally at the point C.

We know that if two circles touches each other either externally or internally, then the centres of the circles and the point of contact lie on the same straight line.

∴ The points A, O, X, A, B, C and B, Y, O lie on the same straight line each.

Now,

AO+BO+BY+OY

=OA+OY+BY  [as per. figure]

=OA+OX+BY [∵OY=OX= radii of same circle]

=AX+BY  [as per figure AO+OX=AX]

= Radius of the larger circle + Radius of the smaller circle.

= Constant [∵ both the circles are fixed ]

Hence (AO+BO) = constant (Proved)