Question

The larger of two concentric circles has radius 8cm.If a chord of the larger circle is tangent to the smaller circle has length 4√14 cm,what is the radius of smaller circle

Answer 1

Answer:

6cm

i hope it may help you

Answer 2

Answer:

The radius of smaller circle is 2√2  cm .

Step-by-step explanation:

Given as :

The radius of the larger circle = R = 8 cm

Let The radius of the smaller circle =  r cm

The tangent of the smaller circle is the chord of the larger circle

The measure of the chord of the larger circle = 4√14  cm

According to question

From figure ,

A concentric circle with center O

The radius of smaller circle = OE = r cm

The radius of the larger circle = OC = OD = R = 8 cm

The length of the chord of the larger circle = CD = 4√14  cm

So, The radius of larger circle make right angle at center O

From the property of right angled triangle

OD² = OE² + ED²

∵ CD = 4√14 cm

∴  ED = 2√14     (ED is half of CD)

So, OD² = OE² + ED²

Or, 8² = OE² + (2√14)²

Or, 64 - 56 =  OE²

Or, OE² = 8

∴  OE = √8

i.e OE = 2√2  cm

So, The radius of smaller circle = OE =  2√2  cm

Hence, The radius of smaller circle is 2√2  cm . Answer