Question

In the given figure, C₁ and C₂ are the two concentric circles having centre 'O'. The radius of the circle C₁ is R₁ 8 cm and that 1 = of C₂ is R2 17 cm. The tangent AB for C₁ = is the chord of circle C₂. The length of the chord AB is​

Answer 1

Step-by-step explanation:

Given:In the given figure, C₁ and C₂ are the two concentric circles having centre 'O'. The radius of the circle C₁ is R₁ 8 cm and that of C₂ is R2 17 cm. The tangent AB for C₁ is the chord of circle C₂.

To find: The length of the chord AB is ?

Solution:

We know that radius make 90° at the intersection point of tangent.

Perpendicular from circle divides the chord in two equal parts.

Thus,

∆OMA is right triangle,right angle at M.

Apply Pythagoras theorem

AO² = OM² + AM²

(17)²=(8)²+ AM²

289=64+AM²

AM²=225

AM=15 cm

Perpendicular from circle divides the chord in two equal parts.

So,

AB=2AM

AB=2×15

AB=30 cm

Final answer:

Length of chord AB is 30 cm.

Hope it helps you.

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