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In Figure, circle C(O ,r)a n dC(O^(prime...

In Figure, circle `C(O ,r)a n dC(O^(prime)r/2)` touch internally at a point. `Aa n dA B` is a chord of the circle `C(O , r)` intersecting `C(O^(prime), r/2)` at `C` . Prove that `A C=C B`

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Join OA,OC and OB
In` /_\OCA `and` /_\OCB `
OA=OB ( Radius of the circle)
`/_OCA=/_OCB=90^0 `(from fig)
`OC=OC` (common side)
By RHS criterion of congruence
`/_\OCA ~= /_\OCB `
`:. AC=CB `
...
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