Two circles with centres `A and B` of radii `3 cm and 4 cm` respectively intersect at two points `C and D` such that `AC and BC` are tangents to the two circles. Find the length of the common chord `CD`.

Explanation

`angle OPO^{prime}=90^{circ}` [Tangent at a point on the circle Is perpendicular to the radius through point of contact]


Therefore, `OPO` is a right-angled triangle at` P`


Using Pythagoras, In triangle` OPO',`


`(OO^{prime})^{2} =(O^{prime} P)^{2}+(OP)^{2}`


`(OO^{prime})^{2}=(4)^{2}+(3)^{2} `


`(OO^{prime})^{2}=25 `


`OO^{prime}=5 cm`


Assume `ON =x cm and NO^{prime}=5-x cm`


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