Question

A quarter of the circle is shown in the figure and another circle is inscribed in it. The length of AB is 2√2 cm.
What is the circumference of the smaller circle?

a) 2√2π cm
b) 2√2π/(1+√2) cm
c) 4√2π cm
d) 4√2π/(1+√2) cm​

Answer 1

Answer:

a is answer

Step-by-step explanation:

it is help for you

Answer 2

Let radius of inscribed circle be x

[ AB and BC are tangents to the inscribed circle ]

Explanation of diagram :-

▶️ OM = ON ( radius of same circle )

▶️ BP = AB = BC ( radius of quater of circle )

▶️ Now, in quadrilateral MONB , all the angles measure 90° and sides OM and ON are equal. Therefore , the given quadrilateral is a square.

Now , first we will find out diagonal OB of square MONB.

➡️OB² = BN² + ON²

➡️OB² = x² + x²

➡️OB² = 2x²

➡️OB = √2 x

Now, OB + OP = BP

➡️ OB + OP = 2√2 ( AB = BP = 2√2)

➡️ √2 x + x = 2√2

➡️ (√2 +1) x = 2√2

➡️ x =( 2√2 )/ (√2 +1)

radius of inscribed circle = ( 2√2 )/ (√2 +1) cm

Circumference of circle = 2π × radius

➡️Circumference of circle =2π × ( 2√2 )/ (√2 +1)

➡️Circumference of circle = (4π√2 )/ (√2 +1) cm

Answer :-

option (d) 4√2π/(1+√2) cm is correct