Question

two concentric circle of radii 10 cm and 8cm find the length of chord of larger circle which towel smaller circle two concentric circle of radii 10 cm and 8cm find the length of chord of larger circle which towel smaller circle

Answer 1

Answer:

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Answer 2

Given,

For two concentric circles;

The radius of the outer circle = 10 cm

The radius of the inner circle = 8 cm

To find,

The length of the chord of the larger circle that touches the smaller circle.

Solution,

We can simply solve this mathematical problem using the following process:

Let us assume that the length of the chord of the larger circle which touches the smaller circle is x cm.

Geometrically,

In a set of concentric circles, the chord of the larger circle which touches the smaller circle at a single point on the smaller circle is perpendicular to the smaller circle's radius at that single point. This point is also the midpoint of that chord.

This implies, half of the chord of the larger circle, which touches the smaller circle, and the radio of both the circles form a right-angled triangle. The radius of the larger circle forms the hypotenuse.

{Equation-1}

Now, according to the question;

applying Pythagoras theorem, we get;

(length of the chord of the larger circle which touches the smaller circle/2)^2 + (radius of the smaller circle)^2

= (radius of the larger circle)^2

=> (x/2)^2 = (10)^2 - (8)^2 = 100 - 64

=> (x/2)^2 = 36 = (6)^2

=> x/2 = 6

=> x = 12 cm

Hence, the length of the chord of the larger circle which touches the smaller circle is equal to 12 centimeters.