Question

In the figure shown, the bigger circle has radius 1 unit. Therefore, the radius of smaller circle must be

Answer 1

Step-by-step explanation:

Given

In the figure shown, the bigger circle has radius 1 unit. Therefore, the radius of smaller circle must be

OBCA is a square drawn inside circle and OC extended to D is diagonal.

Let the radius of bigger and smaller circles be R1 and R2

Given R1 = 1 unit

AC = BC = CD = OA = OB = R1 and OD = R2

Now OC = OD – CD

             = R1 – R2

In triangle OBC, by Pythagoras theorem we get

OC^2 = BC^2 + OB^2

(R1 – R2)^2 = R2^2 + R^2

R1^2 – 2 R1R2 + R2^2 = 2 R2^2

R1^2 – 2 R1 R2 – R2^2 = 0

We know that  

x = - b + - √b^2 – 4ac / 2 a

R2 = -2 R1 + - √(2R1)^2 – 4 (1)(-R1^2) / 2 x 1

R2 = - 2 R1 + - √4 R1^2 + 4R1^2 / 2

R2 = - 2 R1 + √8 R1^2 / 2

R2 = - 2R1 + 2R1√2 / 2

R2 = - R1 + R1√2

R2 = (√2 – 1)R1

R2 = √2 – 1 unit (Since R1 = 1 unit)

Answer 2

Answer:

you can answer this by following steps given

Step-by-step explanation:

hence , the r = 1+sqrt(root) 2