Two concentric circles are of radii 7 cm and 'r' cm respectively, where r 7 A chord of - Maths - Areas Related to Circles

Question

Two concentric circles are of radii 7 cm and 'r' cm
respectively, where r >7 A chord of the larger circle, of length
48 cm, touches the smaller circle Find the value of 'r' ?

Lalit Mehra · Accepted Answer

Let O be the centre of the concentric circles. AB is the chord of the larger circle and tangent to the smaller circle at D.

Given, OD = 7 cm, OB = r cm and AB = 48 cm

AB is the tangent to the smaller circle.

∴ ∠ODB = 90° (Radius is perpendicular to the tangent at point of contact)

OD⊥AB,

$∴ AD = BD = \frac{AB}{2} = \frac{48 cm}{2} = 24 cm (Perpendicular from the centre to the chord bisects the chord)$

In ΔODB,

OB² = OD² + BD²

$∴ r^{2} = (7 cm)^{2} + (24 cm)^{2} = 49 {cm}^{2} + 576 {cm}^{2} = 625 {cm}^{2}$

$\Rightarrow r = \sqrt{625} cm = 25 cm$

Thus, the value of r is 25 cm.

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Two concentric circles are of radii 7 cm and 'r' cm respectively, where r >7 .A chord of the larger circle, of length 48 cm, touches the smaller circle. Find the value of 'r' ?