The question is from the topic circles. From the diagram, we have to find out the circumference of the circle. A perpendicular to the diagram of the circle and it's distance is given. CAT Geometry questions are heavily tested in CAT exam. Make sure you master Geometry problems.
Question 31: What is the circumference of the below circle given that AB is the diameter and XY is perpendicular to AB?
Join AY and let AX = a
Diameter = a + 3
Since AB is the diameter, ∠AYB = 90∘
Since XY is perpendicular to AB, ∠BXY = 90∘
BY = √(32+52) = √34
Consider triangles ABY and BXY
∠ABY is same as ∠XBY and both the triangles are right angled
Therefore they are similar triangles and sides are proportional!
AB/BY = BY/BX = AY/XY
(a+3)/√34 = √34/3
3a + 9 = 34
or a = 25/3
Diameter = 25/3 + 3 = 34/3
Circumference = π * d = 34π/3 cm
The question is "What is the circumference of the below circle given that AB is the diameter and XY is perpendicular to AB?"
Choice C is the correct answer.
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