Question

two circles of radii 5cm and 3cm intersect at 2 points and the distance between their centers is 4cm. find the common chord.

please attach a pic. ​

Answer 1

Answer:

Common chord = 6 cm

Step-by-step explanation:

Given:

Two circles of radii 5cm and 3cm intersect at 2 points and the distance between their centers is 4cm.

To Find:

Find the common chord.

Solution:

If two circles intersect each other at two points, then the line joining their centres is the perpendicular bisector of the common cord.

OO' will be the perpendicular bisector of chord AB

⇒ AC = CB

Let OC be x.

Therefore, O'C will be 4 - x.

In ΔOAC,

OA² = AC² + OC²

==> 5² = AC² + x²

==> 25 - x2 = AC²   ----- (1)

Now, In ΔO'AC,

O'A² = AC² + O'C²

==> 32 = AC² + (4 - x)²

==> 9 = AC² + 16 + x² - 8x

==> AC² = - x² - 7 + 8x   ----- (2)

From (1) and (2), we get

==> 25 - x² = - x² - 7 + 8x

==> 8x = 32

==> x = 4

Hence, O'C = 4 - 4 = 0 cm.

and hence, it will be the diameter of the smaller circle.

Also, AC² = 25 - x²

==> AC² =  25 - 4²

==> AC² = 25 − 16

==> AC² = 9

==> AC = 3 cm

Length of the common chord AB = 2 AC = 6 cm

Result:

Common chord = 6 cm.

#BeBrainly

Answer 2

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