Question

O is the center of two concentric circles of radii 13cm and 5cm.if AB is a tangent of inner circle, then AB=___ explanation ​

Answer 1

Given info : O is the centre of two concentric circles of radii 13cm and 5cm.

To find : the tangent of inner circle AB.

Solution : see diagram as shown in figure, here it is clearly mentioned that AB is tangent of inner circle. We know, radius is always perpendicular on tangent. So, OM perpendicular to AB

So ∆OMB is a right angled triangle.

from Pythagoras theorem,

OB² = OM² + MB²

⇒(13cm)² = (5cm)² + MB²

⇒169cm² - 25cm² = MB²

⇒MB² = 144 cm² = (12 cm)²

⇒MB = 12cm

But MB = AM

so, AB = AM + MB = 12cm + 12cm = 24

Therefore the tangent of inner circle AB is 24 cm

Answer 2

Answer:-

Given info :

O is the centre of two concentric circles of radii 13cm and 5cm.

To find :

the tangent of inner circle AB.

Solution :

see diagram as shown in figure, here it is clearly mentioned that AB is tangent of inner circle. We know, radius is always perpendicular on tangent.

So,

OM perpendicular to AB

So ∆OMB is a right angled triangle.

from Pythagoras theorem,

OB² = OM² + MB²

⇒(13cm)² = (5cm)² + MB²

⇒169cm² - 25cm² = MB²

⇒MB² = 144 cm² = (12 cm)²

⇒MB = 12cm

But MB = AM

so,

AB = AM + MB = 12cm + 12cm = 24

Therefore the tangent of inner circle AB is 24 cm

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