Question

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

Answer 1

Figure:-

Given:-

• Two circle of radii 5cm and 3cm intersect at two points and the distance between their centres is 4cm.

To find:-

• find the length of the common chord

Solutions:-

• Let the radius of the circle centered at O and O' be 5cm and 3cm.

OA = OB = 5cm

O'A = O'B = 3cm

O'O is the perpendicular bisector of chord AB.

.:. AC = CB

O'O = 4cm

Let OC be x.

Therefore,

O'C be x - 4

In ∆OAC,

OA² = AC² + OC²

5² = AC² + x²

25 = AC² + x² .....................(i).

In ∆O'AC,

O'A² = AC² + O'C²

3² = AC² + (x - 4)²

9 = AC² + x² + 16 - 8x

AC² = -x² - 7 + 8x .............(ii).

From Eq (i). and (ii). we get.

25 - x² = - x² - 7 + 8x

8x = 32

x = 4

The Common chord is pass through the centre of the smaller circle and the diameter of the smaller circle.

Length of the common chord AB.

AB = 2O'A

AB = 2 × 3 cm

AB = 6cm.

Hence, the length of the common chord is 6cm..

Answer 2

hope it's helpful for u........