Two equal circles pass through each other’s centre. If the radius of each cirlce is 5 cm,what is the length of the common chord?
Let O be the mid point between the centres. So , AO=OB=2.5
Let C be one of the intersecting points of the circles. AC=5
OC= $$\sqrt{AC^2 - OA^2}$$
OC= $$\sqrt{5^2 - 2.5^2}$$
= $$\frac{5\sqrt{3}}{2}$$
Length of cord = $$2\times\frac{5\sqrt{3}}{2}$$
= $$5\sqrt{3}$$
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