Question

Two concentric circles are of radii 5 cm and 3 cm. Find the length of the chord of larger circle which touched the smaller circles

Answer 1

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Answer 2

Solution:

• Draw two concentric circles with the centre O.
• Now, draw a chord AB in the larger circle which touches the smaller circle at a point P as shown in the figure below.

From the above diagram, AB is tangent to the smaller circle to point P.

∴ OP ⊥ AB

Using Pythagoras theorem in triangle OPA,

OA² = AP² + OP²

=> 5² = AP² + 3²

=> AP² = 25 – 9 = 16

=> AP = 4

OP ⊥ AB

Since the perpendicular from the centre of the circle bisects the chord, AP will be equal to PB

So, AB = 2AP = 2 × 4 = 8 cm

Hence, the length of the chord of the larger circle is 8 cm.