CAT Quantitative Aptitude Questions | Geometry Questions for CAT - Triangles

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?

1. 8π cm
2. π√34 cm
3. 34π/3 cm
4. π√31/3 cm

Explanatory Answer

Method of solving this CAT Question from Circles: Finding the radius of the circle will help! Look at the triangles present!.

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?"

Hence, the answer is 34π/3 cm.

Choice C is the correct answer.