Question

If two circles are cut each other then their common chord is called

Answer 1

Answer:

Common chord of two intersecting circles is the line segment joining points of intersection of two circles.

Check the figure above for better understanding.

Answer 2

Answer:

If two circles are cut each other then their common chord is called the line segment joining points of the intersection of two circles.

Step-by-step explanation:

Common chord:

  A common chord of two intersecting circles is called the line segment joining the point of intersection of two circles.

Note:

• Intersecting circles line joining the centers cut the chord at its midpoint and are perpendicular to it.

• The radius of both circles, half chord, and line joining the two centers make two right-angled triangles whose hypotenuse is the radius.

Example :

Q) Two circles of radii 10cm and 8cm intersect and the length of the common chord is 12cm. What is the distance between their centers?

Solution:

Given radii r₁= 10cm, r₂= 8cm

and length of common chord = 12cm

we know that intersecting circles line joining the centers cut the chord at its midpoint and are perpendicular to it.

So, the radius of both circles, half chord, and line joining the two centers make two right-angled triangles whose hypotenuse is the radius.

• In the first right-angled triangle.

           h = 10cm,    

                   First side = 12/2 = 6 cm,

              Second side = $\sqrt{(10)^{2} -(6)^{2} }$ = 8cm

• In the second right-angled triangle,

           h = 8cm,

                First side = 6cm

           Second side = $\sqrt{(8)^{2} -(6)^{2} }$ = $\sqrt{28}$ cm

• Distance between centers = 8 + $\sqrt{28}$ cm = 8 + 2 $\sqrt{7}$ cm

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