Question

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Two circles of radii 5 cm and 3 cm intersect at two points and the distance between their centres is 4 cm. Find the length of the common chord.​

Answer 1

Answer:

Given that the circles intersect at two points, so we can draw the above figure.

Let AB be the common chord. Let O and O’ be the centers of the circles, respectively.

O’A = 5 cm, OA = 3 cmOO’ = 4 cm [Given distance between the centres is 4cm]

Since the radius of the bigger circle is more than the distance between the 2 centers,

we can say that the center of the smaller circle lies inside,

the bigger circle itself.OO’ is the perpendicular bisector of AB.So, OA = OB = 3 cmAB = 3 cm + 3 cm = 6 cm

[Since, O is the mid point of AB]

The length of the common chord is 6 cm.It is also evident that the common chord is the diameter of the smaller circle.