What is the circumf...

Share:
Clear all

# What is the circumference of the below circle given that AB is the diameter and XY is perpendicular to AB?

(@soham)
Estimable Member

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
Topic starter Posted : 23/03/2021 8:36 pm
(@rahul)

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.
Posted : 23/03/2021 9:03 pm
Share: