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Two perpendicular lines that intersect each other at the centre of a circle of radius 1 unit divides the circle into four parts. A smaller circle is inscribed in one of those parts as shown in the figure below. What is the radius of the smaller circle?
  • a)
    √2 + 1
  • b)
    √2 - 2
  • c)
    √2 - 1
  • d)
    √2 + 2
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
Two perpendicular lines that intersect each other at the centre of a c...
Let x denote the radius of the smaller circle. The figure shows the lengths marked to the right as follows.
Here,
BO2 = AB2 + AO2
BO2 = x2 + x2
BO = √2x
BO + OC = 1
Hence, this is the correct answer.
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Two perpendicular lines that intersect each other at the centre of a circle of radius 1 unit divides the circle into four parts. A smaller circle is inscribed in one of those parts as shown in the figure below. What is the radius of the smaller circle?a)√2 + 1b)√2 - 2c)√2 - 1d)√2 + 2Correct answer is option 'C'. Can you explain this answer?
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