# CAT Practice : Coordinate Geometry

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Finding the radius of the circle will help! Look at the triangles present!

## Circumference of a circle

Q.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 ${\surd 34}$ cm
3. 34π/3 cm
4. π ${\surd 31}$/3 cm

Choice (C). 34π/3 cm

## Detailed Solution

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 = ${\surd (3^2 + 5^2)}$ = ${\surd 34}$

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)/${\surd 34}$ = ${\surd 34}$/3
3a + 9 = 34
or a = 25/3
Diameter = 25/3 + 3 = 34/3
Circumference = π*d = 34π/3 cm

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Geometry is probably the most vital topic as far as CAT preparation is concerned. Geometry sets the stage for Trigonometry, Cogeo and Mensuration as well.