Question

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

Answer 1

Let the larger circle have its center at L and let the center of the smaller circle be S. Let the points of intersection of the circles be A and B. Let the common chord AB intersect the line joining the centers L and S at P.

LA = LB = 5cm. SA = 3cm. LS = 4cm.

Thus LAS and LBS are right-angled triangles with the right angle at P (actually, P coincides with S). Thus AP (or rather AS) will be half the common chord and the common chord AB will be 2* SA which is 6 cm and so your answer.

Answer 2

Hi there!

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For solutions, Refer to the attached picture.
Regrets for handwriting _/\_

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Let's see some related topics :

⚫ Circle : The collection of all the points, which are at a fixed distance from a fixed point in a plane, is called a circle.

⚫ Radius : A line joining the centre to the Circumference of the circle, is called radius of a circle.

⚫ Secant : A line intersecting a circle at any two points, is called secant.

⚫ Diameter : A chord passing through the point of the circle, is called diameter. It is the longest chord.

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Thanks for the question !

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