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?

- 8π cm
- π√34 cm
- 34π/3 cm
- π√31/3 cm

34π/3 cm

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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 = √(3^{2}+5^{2}) = √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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