Mathematics

The radii of two concentric circles are 6 cm and 10 cm respectively. Find the length of the chord of the bigger circle which is tangent to smaller circle.

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From figure,

There are two circles with center A and radius AE = 10 cm and AB = 6 cm.

In △ABE,

⇒ AE² = AB² + BE²

⇒ 10² = 6² + BE²

⇒ 100 = 36 + BE²

⇒ BE² = 100 - 36

⇒ BE² = 64

⇒ BE = $\sqrt{64}$ = 8 cm.

We know that,

The perpendicular from the centre to a chord bisect the chord.

DE = 2BE = 2 × 8 = 16 cm.

Hence, length of chord of bigger circle which is tangent to smaller circle = 16 cm.

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