Question

Two concentric circles of radius 10 cm and 8cm then the length of the chord of the larger circle which touches the smaller circle is​

Answer 1

Two circles of radius 8 cm and 10 cm, with the same center, are drawn.

A tangent to the smaller circle is drawn.

Let the chord be x.

The two radii and the bisected tangent form a right triangle, with the longer radius being the hypotenuse.

→ $\sf{(\dfrac{x}{2} )^2+8^2=10^2}$

→ $\sf{\dfrac{x^2}{4} +64=100}$

→ $\sf{\dfrac{x^2}{4} =36}$

→ $\sf{x^2=144}$

$\sf{\therefore x=12}$ cm is the chord.

Learn more:

The reason the tangent is bisected is because of the chord properties.

A perpendicular bisector of a chord will pass through the center of the circle.

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